Lecture Notes in Computer Science 7777Commenced Publication in 1973Founding and Former Series Editors:Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board

David HutchisonLancaster University, UK

Takeo KanadeCarnegie Mellon University, Pittsburgh, PA, USA

Josef KittlerUniversity of Surrey, Guildford, UK

Jon M. KleinbergCornell University, Ithaca, NY, USA

Alfred KobsaUniversity of California, Irvine, CA, USA

Friedemann MatternETH Zurich, Switzerland

John C. MitchellStanford University, CA, USA

Moni NaorWeizmann Institute of Science, Rehovot, Israel

Oscar NierstraszUniversity of Bern, Switzerland

C. Pandu RanganIndian Institute of Technology, Madras, India

Bernhard SteffenTU Dortmund University, Germany

Madhu SudanMicrosoft Research, Cambridge, MA, USA

Demetri TerzopoulosUniversity of California, Los Angeles, CA, USA

Doug TygarUniversity of California, Berkeley, CA, USA

Gerhard WeikumMax Planck Institute for Informatics, Saarbruecken, Germany

Harout Aydinian Ferdinando CicaleseChristian Deppe (Eds.)

Information Theory,Combinatorics,and Search Theory

In Memory of Rudolf Ahlswede

13

Volume Editors

Harout AydinianChristian DeppeUniversity of BielefeldDepartment of MathematicsUniversitätsstr. 25, 33615 Bielefeld, GermanyE-mail: {ayd, cdeppe}@math.uni-bielefeld.de

Ferdinando CicaleseUniversity of SalernoDepartment of Computer Sciencevia Ponte don Melillo, 84084 Fisciano, ItalyE-mail: cicalese@dia.unisa.it

ISSN 0302-9743 e-ISSN 1611-3349ISBN 978-3-642-36898-1 e-ISBN 978-3-642-36899-8DOI 10.1007/978-3-642-36899-8Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2013933137

CR Subject Classification (1998): E.4, G.2.1-2, F.2.2

LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues

© Springer-Verlag Berlin Heidelberg 2013This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,in ist current version, and permission for use must always be obtained from Springer. Violations are liableto prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,even in the absence of a specific statement, that such names are exempt from the relevant protective lawsand regulations and therefore free for general use.

Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Rudolf Ahlswede

1938 – 2010

Preface

The Center for Interdisciplinary Research (ZiF) at the University of Bielefeldhosted a cooperation group under the title “Search Methodologies”, fromOctober 1, 2010 to December 31, 2012. The main aim of the cooperation group“Search Methodologies” was to gain a deep understanding of the fundamentalmathematical structures shared by different models of search encountered inmany fields of the hard sciences and the natural sciences. The starting pointwas the discovery that certain mathematical structures and methodological ap-proaches that we identify as typical of search problems are found in surprisinglydiverse scenarios and areas that are, a priori, considered not connected to thefield of combinatorial search.

One of our goals has been to create a common forum for theoreticians butalso practitioners for comparing different approaches to search problems anddifferent fields of application of search paradigms.

The ZiF cooperation group started in 2010 promoted and led by RudolfAhlswede and Ferdinando Cicalese. The seeds of this project had been planted ina preceding Dagstuhl seminar on “Search Methodologies”, organized byR. Ahlswede, F. Cicalese, and U. Vaccaro, and held at the Leibniz Institut ofDagstuhl July 5–10, 2009. In fact, the opening conference of the ZiF cooperationgroup was named “Search Methodologies II”, held on October 25–29, 2010.

As clearly stated by Rudolf Ahlswede in the opening lecture of this conference,the time was ripe for founding a comprehensive general theory of search.

Sadly, Rudi will not be able to see the full development of this plant hehas so much and devotedly contributed to. On December 18, 2010, suddenly andunexpectedly, Rudolf Ahlswede passed away, but the project continued thanks tothe effort of Christian Deppe (who took over as co-organizer), Harout Aydinian,and Vladimir Lebedev. This book is meant as a memorial and includes papersdedicated to Rudolf Ahlswede and results of the cooperation group “SearchMethodologies”.

On July 25 and 26, 2011 a memorial symposium for Rudolf Ahlswede tookplace at the ZiF at the University of Bielefeld. The symposium was organizedin close cooperation with Rudolf Ahlswede’s former students and partners of hismany research projects. About 100 participants came to Bielefeld to rememberthe life and the work of Rudi, the great mathematician, the friend, the mentor,the man.

“Search Methodologies III” was the closing event of the cooperation group.The list of the four macro-topics of this workshop—theory of games and strate-gic planning, combinatorial group testing and database mining, computationalbiology and string matching, information coding and spreading and patrollingon networks—provides a comprehensive picture of the vision Rudolf Ahlswedehad and put forward of a broad and systematic theory of search.

VIII Preface

This book includes 36 thoroughly refereed research papers dedicated to thememory of Rudolf Ahlswede and the research areas in which he worked and that,in several cases, he contributed to shape. One third of the papers originatedwithin the framework of the ZiF cooperation group “Search Methodologies”.Furthermore three obituaries and several stories and anecdotes related to RudolfAhlswede’s life are included.

We are deeply grateful to the members of the administration of the ZiF inBielefeld for their invaluable and always extremely kind and patient cooperation.

November 2012 Harout AydinianFerdinando Cicalese

Christian Deppe

Organization

Referees

Harout AydinianBernhard BalkenholIgor BjelakovicVladimir BlinovskyHolger BocheMiklos BonaJeremie BourdonMinglai CaiNing CaiHong-Bin ChenFerdinando CicaleseEva CzabarkaImre CsiszarChristian DeppeChristian DonningerArkadii D’yachkov

Konrad EngelPeter ErdosJanos FollathNathan GartnerDaniel GerbnerOleg GranichinKatalin GyarmatiPawel HitczenkoThomas KalinowskiKeiichi KanekoGyula KatonaKingo KobayashiGerhard KramerEyal KushilevitzVladimir LebedevUwe Leck

Robert LeonardLinyuan LuHeinrich MatzingerFranz MerklBalazs PatkosVyacheslav RykovOriol SerraUlrich TammEberhard TrieschMoritz WieseAndreas WinterJurg WullschlegerSergey YekhaninZhen Zhang

Supporting Institutions

Fakultat fur Mathematik (Department of Mathematics)Universitat BielefeldPostfach 100131D-33501 BielefeldGermany

Zentrum fur interdisziplinare Forschung (ZiF)(Center for Interdisciplinary Research)Universitat BielefeldWellenberg 133615 BielefeldGermany

More than restoringstrings of symbols transmittedmeans transfer today

What is information?

Cn bits in Shannon’s fundamental theoremor log Cn bits in our Theory of Identification ?

Time is maturefor a general Theory of Search.

When we speak of General Theory of Information Transfer todaywe mean it to include at its core

the theory of information transmission,common randomness, identification and

its generalizations and applications,but it goes far beyond it even outside communication theory

when we think about probabilistic algorithms with identificationas concepts of solution!

Close to the Shannon Island we can see1.) Mathematical Statistics2.) Communication Networks3.) Computer Storage and Distributive Computing4.) Memory CellsSince those islands are close there is hope that they can be connected by dams.

There are various stimuli concerning the concepts of communicationand information from the sciences,

for instance from quantum theory in physics,the theory of learning in psychology, theories in linguistics, etc

We live in a world vibrating with informationand in most cases we dont knowhow the information is processed

or even what it is at the semantic and pragmatic levels.

It seems that the whole body of present dayInformation Theory will undergo serious revisions

and some dramatic expansions.

Rudolf Ahlswede

1 Introduction

Above are some quotations directly taken from Rudolf Ahlswede’s talks, pre-senting his scientific vision. This is probably the best way to start a volumededicated to his invaluable contribution to our community. The scientific arti-cles included in this volume are organized according to a broad classification ofAhlswede’s interests into three main areas: Information Theory, Combinatorics,Search Theory. The boundaries of such classification are necessarily fuzzy andmany papers might well fit into two or all of such major areas, very much likemost of Ahlswede’s work.

The papers were thoroughly refereed; in the following they are referred to bynumber, preceded by the letter B, to indicate the present book. We refer to twoother lists of publications. They are labelled A and I, where

A indicates the list of publications of Rudolf Ahlswede at the backmatter ofthe book

I is used for papers mentioned in the introduction, in particular in these com-ments

The volume is concluded by several obituaries and anecdotes about RudolfAhlswede’s life written by friends and coauthors.

Papers related to Rudolf Ahlswede’s work

Here are some numerical facts about Rudolf Ahlswede’s prolific work, with aclassification of his 242 papers according to the main research area each paperaddresses:

area number of papers percentageInformation Theory 138 ∼ 57%- probabilistic models 56 ∼ 23%- combinatorial models, coding theory 29 ∼ 12%- related to search 21 ∼ 8%- flows in networks 8 ∼ 3%- cryptography as dual 9 ∼ 3%- statistics 7 ∼ 3%- memories 5 ∼ 2%- quantum theoretical 7 ∼ 3%

Mainly Combinatorial Structures 104 ∼ 43%-combinatorial extremal problems 64 ∼ 26%-combinatorial number theory 16 ∼ 7%-inequalities (combinatorial - but also probabilistic,number theoretic, analytical) 11 ∼ 5%-computing and complexity(esp. communication complexity) 13 ∼ 5%

XII Introduction

The complete list of Ahlswede’s publications can be found at the end of thisbook. Here are listed the thirty papers with the highest number of citations(source: Google Scholar, Oct. 2012):

[A155]4529

[A12]473

[A79]437

[A18]232

[A21]215

[A122]149

[A50]142

[A161]137

[A59]130

[A30]121

[A29]106

[A36]103

[A55]101

[A131]91

[A47]89

[A51]87

[A27]72

[A23]67

[A156]53

[A31]51

[A132]49

[A32]46

[A60]45

[A99]38

[A17]38

[A53]37

[A114]36

[A63]36

[A44]35

[A65]31

[A3]30

In fact, Ahlswede’s h-index is 30, however, noticeably, the average numberof citations of these papers is 259. Most of the co-authored papers were writtenwith Ning Cai (49), Levon Khachatrian (45), Zhen Zhang (22), Harout Aydinian(22), Andras Sarkozy (9), Christian Deppe (9), Vladimir Blinovsky (8), MarkPinsker (8), Leonid Bassalygo (7), and Imre Csiszar (6). Altogether, Ahlswedeco-authored papers with more than 70 researchers from all over the world.

In the backmatter one can read more about the importance and the impactof Rudolf Ahlswede’s work.

I Information Theory

One of the main research goals of Rudolf Ahlswede’s was the development of whathe defined as a general theory of information transfer (GTIT) [A220], which in-cludes Shannon’s classical theory of transmission and his theory of identificationas special cases.

A step beyond Shannon’s celebrated theory of communication [I07], the foun-dations for a theory of identification in the presence of noise were laid togetherwith Dueck and carried on by Verboven, van der Meulen, Zhang, Cai, Csiszar,Han, Verdu, Steinberg, Anantharam, Venkataram, Wei, Csibi, Yeong, Yang,Shamai, Merhav, Burnashev, Bassalygo, Narayan and many others.

To fix first ideas, the (classical) theory of information transmission is con-cerned with the question of how many different messages we can transmit overa noisy channel. Basically, in a (two-party) communication, the receiver triesto answer the question “What is the actual message sent from the set M ={1, . . . , M}?”

On the other hand in the theory of identification, the problem is about iden-tifying rather than recognizing (or reconstructing) a message sent over a (noisy)channel. In short, one tries to answer the question “Is the actual message sent i?”,where i is some fixed member of the set of possible messages M = {1, 2, . . . , N}.

This change of perspective extends the frontiers of information theory in sev-eral directions and has led to the discovery of new methods which are fruitful alsofor the classical theory of transmission, for instance in studies of robustness, arbi-trarily varying channels, optimal coding procedures in case of complete feedback,novel approximation problems for output statistics and generation of commonrandomness, a key issue in cryptology.

In this volume, some aspects of the theory of identification are studied in [B01]by Christian Heup, one of Ahlswede’s PhD-students. This paper is devoted to

Introduction XIII

the proof of bounds for the expected running time and worst- case running timefor identification process for sources.

[B02] introduces L-Identification as a generalization of identificationfor sources, and the concept of identification entropy of second order as a lowerbound.

Shannon’s paper about two-way communication was the starting point ofmulti-user information theory, an area in which Rudolf Ahlswede worked inten-sively, particularly in collaboration with Ning Cai, who got his PhD under thesupervision of Ahlswede. Their life-long collaboration produced 49 papers alto-gether. Ning Cai’s contribution to this volume is contained in the joint paper[B03] with Binyue Liu. The article studies the following channel problem: twosenders would like to simultaneously transmit a message each to a receiver. Thisis done in two steps. First, the message pair is transmitted to n relays. In thesecond step, the n relays transmit an amplified version of what they received tothe receiver. The receiver does not receive anything in the first step. All chan-nels are subject to additive Gaussian noise. The senders have individual powerconstraints. For the relays two cases are considered. In the first case they havea sum power constraint. In the second case they are subject to individual powerconstraints. The problem treated in the paper is in each case to find the opti-mal amplify-and-forward scheme, i.e. the powers at which the relays forward thereceived signals to the receiver, and to find the corresponding rate region.

In the field of information technology starting around the year 2005, therewas much interest in and discussion of Rudolf Ahlswedes information theoreti-cal approach to the development of future communication systems. Because ofthis, Rudolf Ahlswede was often invited to information technology conferencesas the plenary speaker. He lively exchanged developments with many engineersand this led him to attend research meetings at the TU Berlin and the Hein-rich Hertz Institute, where he worked closely with Holger Boches group. Thefollowing topics were discussed extensively in his lectures and in joint seminars:information theoretic security, arbitrary varying classical and quantum chan-nels, common randomness and de-randomization, resource theory for classicaland quantum channels, multiuser systems, new approaches for frequency usage,and approaches to model channel uncertainty. Rudolf Ahlswede was also verymuch interested in the practical aspects of communication systems, and theresulting discussions led to many publications. This tradition of his close coop-eration with communication engineers that had its beginnings in Berlin was tohave been continued with his appointment to the Institute of Advanced Studyat the TU Munchen in 2011.

Moritz Wiese, one of Boche’s group, and Holger Boche considered a multi-user model in [B04]. The multiple access channel with eavesdropper is consideredwith two main variations: with common randomness (between the transmitters)and with rate-limited conferencing. In addition, in the first variant, the sendersnot only have their own message but also have to transmit a common one. Itcomes to no surprise that the problem is complex, and the present authors don’t

XIV Introduction

completely solve it. But they use some well-established bits of machinery andquite some ingenuity to provide achievable regions.

This paper introduces us to another important research area to which Ah-swede gave a significant contribution: cryptography. In this field, the article byIgor Bjelakovic, Holger Boche, and Jochen Sommerfeld [B05] presents severalresults on AVCs and wiretapping: a lower bound on the random code secrecycapacity for the average error criterion and the strong secrecy criterion in thecase where of the eavesdropper has the best channel; an upper bound on thedeterministic code secrecy capacity in the general case, which results in a multi-letter expression for the secrecy capacity in the case of best channel for theeavesdropper.

A third paper on cryptography is by Csiszar (joint work with RudolfAhlswede). In [B06] the author shows new results on the so-called oblivioustransfer (OT) capacity in the honest-but-curious model. OT is a fundamentalconcept in cryptography, see for example [I04]. The term has been used withdifferent meanings, including a simple transmission over a binary erasure chan-nel. Here OT means “1-2 oblivious string transfer” [I04]: Alice has two length-kbinary strings K0 and K1 and Bob has a single bit Z as inputs; an OT pro-tocol should let Bob learn KZ while Alice remains ignorant of Z and Bob ofKZ (Z = 1−Z). The Shannon-theoretic approach is used, thus ignorance meansnegligible amount of information. In 1988 Rudolf Ahlswede received togetherwith Imre Csiszar the Best Paper Award of the IEEE Information Theory Soci-ety for work in the area of the hypothesis testing.

Another major breakthrough brought by Rudolf Ahlswede to the area of in-formation theory was the definition of network coding in [A155]. Network codingis by now a generally accepted concept and has started a revolution in commu-nication networks! We quote from page 58 of [I03] “On the Internet and othershared networks, information currently gets relayed by routers – switches thatoperate at nodes where signaling pathways, or links, intersect. The routers shuntincoming messages to links heading toward the messages’ final destinations. Butif one wants efficiency, are routers the best devices for these intersections? Isswitching even the right operation to perform?

Until seven years ago, few thought to ask such questions. But then RudolfAhlswede of the University of Bielefeld in Germany, along with Ning Cai, Shuo-Yen Robert Li and Raymond W. Yeung, all then at the Chinese University ofHong Kong, published groundbreaking work that introduced a new approach todistributing information across shared networks. In this approach, called networkcoding, routers are replaced by coders, which transmit evidence about messagesinstead of sending the messages themselves. When receivers collect the evidence,they deduce the original information from the assembled clues.

Although this method may sound counterintuitive, network coding, which isstill under study, has the potential to dramatically speed up and improve thereliability of all manner of communications systems and may well spark the nextrevolution in the field. Investigators are, of course, also exploring additional

Introduction XV

avenues for improving efficiency; as far as we know, though, those other ap-proaches generally extend existing methods.”

In [B07] Anas Chaaban, Aydin Sezgin, and Daniela Tuninetti consider thesymmetric butterfly network (BFN) with a full-duplex relay operating in a bi-directional fashion for feedback. This network is relevant for a variety of wirelessnetworks, including cellular systems dealing with cell-edge users. Upper boundson the capacity region of the general memoryless BFN with feedback are derivedbased on cut-set and cooperation arguments and then specialized to the lineardeterministic BFN with really-source feedback.

In [B08] David Einstein and Lee Jones consider the case of a network withgiven total flows into and out of each of the sink and source nodes. It is usefulto select uniformly at random an origin-destination (O-D) matrix for which thetotal in and out flows at sinks and sources (column and row sums) match thegiven data. The authors give an algorithm for small networks ( less than 16nodes) for sampling such O-D matrices with exactly the uniform distributionand apply it to traffic network analysis. This algorithm can also be used in thestatistical analysis of contingency tables.

Ahlswede and Jones were together in Gottingen from 1974 to 1975 and inBielefeld Summer semester 1991. They never published jointly. However theytogether discovered and provided several information-theoretic counterexamplesfor Imre Csiszar. In addition they found several very short original proofs ofprobability theorems (published by others in the mid 1970’s) on partially orderedsets. And for a brief period they claimed an extension of Christofides travelingsalesman inequality to the k-salesmen case (Daniel Kleitman even presentedtheir proof at the Vancouver International 1974 Congress.) Shortly thereafterthey discovered an error in the proof and showed with an example that theextension was impossible. Both agreed not to publish the counterexample asAhlswede (at that time) believed that Science is better advanced with positivenot negative results.

In 1996 Ahlswede started to work intensively on Quantum Information The-ory. He was the supervisor of Andreas Winter who is now one of the main expertsin the field. In the article [B09], Andreas Winter provides a survey of basic con-cepts, and main results in identification over quantum channels. This quantumcounterpart of the classical channel identification was introduced in P. Lober’sPhD thesis, under the supervision of Ahlswede. Andreas Winter’s paper alsoincludes a list of open problems in the area.

In [B10], Vladimir Blinovsky and Minglai Cai – the last student who startedhis PhD under the supervision of Ahlswede – derive a lower bound on the capac-ity of classical-quantum arbitrarily varying wiretap channel. The theory of theclassical-quantum arbitrarily varying channel was developed by Ahlswede andBlinovsky. The complete characterization of the capacity of classical-quantumarbitrarily varying channel was given in [A216]. For the corresponding wiretapchannel the situation is different. Only a lower bound is derived in the paper.The technique for the proof combines ideas from the theory of arbitrarily vary-ing channel with ideas from the theory of the wiretap channel. Furthermore the

XVI Introduction

authors also determine the capacity of the classical quantum arbitrarily varyingwiretap channel with channel state information at the transmitter.

On quantum information theory, Rudolf Ahlswede had established a veryactive collaboration with Holger Boche and his group (see also above). Thiscooperation among the two groups still continues. Their contribution in [B11]deals with compound as well as arbitrarily varying classical-quantum channelmodels. The paper pulls together a whole set of previous results, improving themand simplifying their proofs. Also, the connection between zero-error capacityand certain arbitrarily varying channels is discussed.

At the crossroad of coding and information theory, the area of data compres-sion is also represented in this volume. In [B12] Travis Gagie studies the power ofmultiple read/write streams compared to the single stream case for compression,constrained by polylog memory and passes is considered. The results providedare: universal compression is possible with one stream and one pass; grammarbased compression cannot be achieved with one stream and, regarding streams,entropy-only bounds are achievable iff two streams are available.

The article by Matthias Lowe in [B13] provides a review of the area of sceneryreconstruction, distinguishing sceneries and related topics. This article explainsin a simple manner several of the main mechanisms of the algorithms which havebeen developed in this subfield. The author describes the model as an informationtheretic channel model and ask the question “Can we transmit information oversuch a channel at all?”.

Rudolf Ahlswede entertained a continuing and fruitfull collaboration withArmenian reasearchers at the Institute for Informatics and Automation Prob-lems in Yerevan from beginning of 90’s. Among his collaborators from this insti-tute were Levon Khachatrian, Harout Aydinian, Evgueni Haroutunian and otherreasearchers from the group of Rom Varshamov. Also Ahlswede was the supervi-sor of two PhD students, Marina Kyureghyan and Gohar Kyureghyan, from thatinstitute. During the ZiF project General Theory of Information Transfer andCombinatorics (2001-2004) Ahlswede and Haroutunian investigated problems ofhypothesis testing for arbitrarily varying sources and problems of hypothesisidendification. In [B14] Evgueni Haroutunian and Parandzem Hakobyan sur-vey the investigations on optimal testing of multiple hypotheses, including theresults of Ahlswede and Haroutunian, concerning various multiobject models.These studies show how useful are application of methods and techniques devel-oped in Shannon Information Theory for solution of typical statistical problems.

II Combinatorics

When discussing Ahlswede and Combinatorics, we have to speak of his jointwork with Levon Khachatrian. In 1991 Khachatrian visited the University ofBielefeld, as a guest of the Research Project SFB 343 (Diskrete Strukturenin der Mathematik). In Bielefeld Khachatrian began a very fruitful collabora-tion with Ahlswede, which continued for more than ten years, until the unex-pected death of Khachatrian in early 2002. A series of deep results and solu-tions of long standing problems have been settled by Ahlswede and Khachatrian

Introduction XVII

during this period. Among them two famous problems of Erdos were solved,the first one in number theory, the coprimality problem raised in 1962, and thesecond, in extremal set theory, the intersection problem raised by Erdos, Ko,and Rado in 1938. Combinatorial number theory was one of the favourite sub-jects of Ahlswede and Khachatrian. In the mid 90’s Ahlswede and Khachatrianstarted a close cooperation with the well-known number theorist Andras Sarkozy(the most frequent co-author of Erdos). A series of remarkable joint papers withKhachatrian and Sarkozy, on divisibility (primitivity) of sequences of integers,have been written during this collaboration. Paper [B15] by Christian Mauduitand Andras Sarkozy is dedicated to the memory of Ahlswede and Khachatrian.

[B15] gives a comprehensive survey on the results regarding the f -complexityof sequences. The notion of f -complexity (family-complexity) of sequences wasfirst introduced and studied by Ahlswede, Khachatrian, Mauduit, and Sarkozyin 2003. This quantitative measure of a property of families of sequences tohave “rich“ and “complex” structure plays an important role in cryptography.During the last decade several new papers on f -complexity and related problemshave appeared. [B15] gives a nice overview of those results and related researchproblems. In the last section of the paper the authors answer the question askedby Csiszar and Gacs, at the Ahlswede’s memorial conference (at the ZiF), aboutthe connection between f -complexity and VC-dimension.

In [B16] a shadow minimization problem under word-subword relation is con-sidered for the restricted case. The authors give a complete solution to the prob-lem. This problem was raised by Ahlswede, motivated by the study of capacityerror function for q-ary error-correcting codes with feedback, the subject onwhich Rudolf Ahlswede, Christian Deppe, and Vladimir Lebedev were workingon in late 2010. Vladimir Lebedev cooperated with Ahlswede’s research groupduring the last years visiting regularly the University of Bielefeld.

In [B17] Harout Aydinian, Eva Czabarka, and Laszlo Szekely introduce andstudy k-dimensional M -part multifamilies which is a generalization of M -partSperner families studied in the literature. BLYM type inequalities for these fam-ilies are obtained and connections with multitransversals and mixed orthogonalarrays are established. The convex hull method is extended to k-dimensionalM -part multifamilies which in turn provides new results for Sperner families.Harout Aydinian has worked for many years in the research group of RudolfAhlswede. His joint projects with Ahlswede include topics on extremal combi-natorics, coding theory, and communication networks. Ahlswede and Aydinian,together with Khachatrian, introduced and studied a new type of extremal prob-lems for finite sets: extremal problems under dimensional constraints. Many ofthem are still open.

Rudolf Ahlswede had good relations with many of his co-authors and theirfamilies. Thus, he kept good relations with David Daykin and his family, whichis told in the obituary [B41] by Jacky Daykin, the daughter of David Daykin.David Daykin died in October 2010 and Rudolf Ahlswede gave a talk at hismemorial. One of the last results of David Daykin is [B18]. In this paper, theauthors revisit a well-known problem concerning the factorization of strings in

XVIII Introduction

a Lyndon-like manner. As the main result, they describe efficient sequential andparallel algorithms for factoring of words over some general classes of factoriza-tion families.

One of the last papers of Rudolf Ahlswede is related to a security problemfor databases. In [B19] Sergei Bezrukov, Uwe Leck, and Victor Piotrowski con-sider an interesting combinatorial problem arising in the context of distributeddatabases. For a given configuration T , defined as a set of faulty nodes in ann-dimensional grid graph, the problem asks if (and how fast) is it possible torecover the nodes in T , where an allowed step is to recover all nodes along a linel, parallel to a coordinate axis, as long as l does not contain too many faultynodes. The authors obtained nontrivial bounds for the size of completely recov-erable configurations, for the numbers of steps needed to recover a fixed nodeor the full configuration. They also developed fast recovery algorithms for somevariants of the recovery problem. Sergey Bezrukov, a co-author of Ahlswede, wasa visiting researcher in Ahlswede’s group in the early 90’s.

In [B20] Carlos Hoppen, Yoshiharu Kohayakawa, and Hanno Lefmann lookfor an extremal problem for simple hypergraphs with unique extremal configu-ration but without stability: there are several almost optimal solutions with farapart structures. This phenomenon is known for non- simple graphs, howeverwas not known for simple hypergraphs so far. The problem class studied in thepaper is as follows: fix a family of forbidden hypergraphs F and for a fixed hy-pergraph H and integer k we are looking for all possible k-colorings such thatno monochromatic copy of any element of F is present. The problem is to findthe maximum of this number, over all choises of H . This problem is studiedin details for k = 4 and it is shown that the extremal family is unique whilethe problem (of determining the maximum) is unstable. Hanno Lefmann was astudent and later a colleague of Rudolf Ahlswede at the University of Bielefeld.

The paper [B21] by Ulrich Tamm is devoted to the communication complex-ity problems studied by Ahlswede and his co-authors. Ulrich Tamm was thelast postdoc of Rudolf Ahlswede who did his habilitation at the University ofBielefeld. He was educated by Rudolf Ahlswede as an expert in communica-tion complexity. Motivated by the communication complexity of the Hammingdistance, Ahlswede raised several challenging combinatorial extremal problems(called Two Family Extremal Problems). Some of them are still open. In [B21]first the author surveys some important results on communication complexity ofvector-valued and sum-type functions, for two-party model. In the second parthe shows that some of these results can be extended to a multiparty model forvector-valued functions and the pairwise comparison scheme.

In [B22] Eva Czabarka, Matteo Marsili, and Laszlo Szekely study the thresh-old function to make almost sure that no two bins contain the same number ofballs, when n balls are put into k bins. Depending whether balls and bins aredistinguishable/non-distinguishable, there are four combinations. The authorsdetermined the threshold functions for all four scenarios. The non-distinguishableball problems are essentially equivalent to the Erdos-Lehner asymptotic formulafor the number of partitions of the integer n into k parts.

Introduction XIX

In [B23] Elena Konstantinova gives a survey on two problems of Cayley graphson the symmetric group: the Star graphs and the Pancake graphs. The firstproblem deals with the characterization of efficient dominating sets (or perfectcodes) and the second one on the cycle structure of these two families of graphs.The main contribution of the author is the conclusion that this description coversin fact all possible constructions of perfect codes in these families. Furthermore,the author gives a structural description of small cycles (of lengths between sixand nine) in the Pancake graph.

III Search Theory

When the book [A243] by Rudolf Ahlswede was written in the late 70’s dur-ing the preceding three decades theoretical and practical contributions classifiedas “search” were made in Operation Research, Information Theory, Medicine,Computer Science, Management Science, Optimisation Theory etc. Quite differ-ent tasks were lumped together under the same name and time was not matureto even try a unified theory. Instead, typical examples were treated and this isreflected in the choice of the title.

However, this was at the start of the aim to develop a theory in the long run.We quote “We want to use our concepts and classifications to make a contributionto working out the essential, common points of the various search problems. Bycontrasting the various search problems and the methods for their solution, wehope finally to improve the exchange of information between scientists in thevarious fields.”

This book was divided into several parts each one of them dealing with adifferent class and model of search problems.

At the time of the cooperation group, the following canonical models of searchcould be shown to encompass all of the different classes considered in the book:

Combinatorial Model Probabilistic Model1. X set of objects. 1. (X , P ) search space.2. T ⊂ P(X ) set of tests. 2. W set of stochastical matrices W : X → Y

as set of tests.

Familiar performance criteria are number of errors, error probability, costs,search duration, complexity, ... and expectations thereof (see also [A195]). Non-deterministic strategies are to be also considered.

Going through the fulminant work on search in the last years one noticesa great emphasis on optimisation. If one wants to find the maximum of aninteger-valued function one notices that this search problem is almost in thecanonical form, but not quite: One has to replace objects by sets of objects(putting together functions with the same maximum value). After this slightgeneralisation optimisation is covered by our model and the main issue is tohandle adaptiveness.

One of the main topics in the cooperation group was group testing. In com-binatorial group testing, in an N -element set U , the search space, there is a

XX Introduction

special subset D (the set of defectives of positives, usually |D| � N) which wewant to discover by asking as few tests as possible. A test is any subset A of Uand has two possible outcomes: 0 if A ∩ D = ∅ and 1 otherwise. Adaptive andnon-adaptive strategies have been investigated and also both the cases where anexact estimate or only an upper bound is provided on the size of the set D.

Threshold group testing is a generalization of the basic group testing modelintroduced in [I02]. Let l and u be nonnegative integers with l < u, called thelower and upper threshold, respectively. Suppose that a group test for A saysYes if A contains at least u positives, and No if at most l positives are present.If the number of positives in A is between l and u, the test can give an arbitraryanswer. We suppose that l and u are constant and previously known. The obviousquestions are: What can we figure out about D? How many tests and how muchcomputation are needed? Can we do better in special cases? We call g := u−l−1the gap between the thresholds. The gap is 0 iff a sharp threshold separates Yesand No, so that all answers are determined. Obviously, the classical case of grouptesting is l = 0, u = 1.

Fig. 1. The photo shows Rudolf Ahlswedediscussing with Anna Voronina (PhD ofArkadii D’yachkov) during the conferenceSearch Methodologies II, 2010

In [B24] Rudolf Ahlswede, Chris-tian Deppe, and Vladimir Lebedevconsider non-adaptive threshold test-ing together with another generaliza-tion called majority group testing.They generalize and improve severalearlier results by showing that appro-priate codes are good test sets.

Christian Deppe was the last as-sitant of Rudolf Ahlswede. AfterAhlswede received his emeritus sta-tus, Deppe worked together with himin several projects. Since 2011 he tookthe guidance of the remaining projectsof Ahlswede. Together with HaroutAydinian, Vladimir Blinovsky, Ning

Cai, Minglai Cai, Vladimir Lebedev, and Christian Wischmann he continuesthe work in Bielefeld started by Rudolf Ahlswede. He is thankful for the supportof the Department of Mathematics in Bielefeld and for the help of Holger Bocheand Igor Bjelakovic.

In [B25] Arkadii D’yachkov, Vyacheslav Rykov, Christian Deppe, and VladimirLebedev study superimposed codes and their connections to two non-adaptivegroup testing models introduced by Erlich et al. (2010) and threshold grouptesting. The first part of this paper provides a survey on superimposed codes,which are ubiquitously used for group testing strategies.

D’yachkov first met Ahlswede in 1971 in Tsahkadzor (Armenia) during theSecond International Information Theory Symposium, which was organized inthe USSR. Ahlswede invited D’yachkov several times to Bielefeld.

Introduction XXI

In paper [B26] Rudolf Ahlswede and Harout Aydinian give a construction oferror-tolerant pooling designs, associated with finite projective spaces. A newfamily of dz-disjunct inclusion matrices obtained from packings in finite projec-tive spaces is presented. In particular, a family of disjunct matrices with nearoptimal parameters is obtained.

In [B27] Daniel Gerbner, Balazs Kesegh, Domotor Palvolgyi, and GaborWiener consider a new model of group testing where the set of defectives Dis assumed to be large, but we are only interested in finding at least m of them,where m < |D|. In this model, a test asks if the proportion of the defectiveelements in the subset tested is above a certain threshold. The paper gives lowerand upper estimates on the minimum number of tests (in the worst case) inan adaptive algorithm, which are nearly sharp in different cases of the valuesof the parameters. The first results were presented in the first workshop of thecooperation group and motivated Ahlswede, Deppe, and Lebedev to work on it.Their results on this model were already published in [A237].

In [B28] Hong-Bin Chen and Hung-Lin Fu consider the case where more thanone type of defectives are present in the search space and the result of a testcan be affected by the simultaneous presence of different types of defectives. Theauthors provide lower and upper bounds on the total number of tests required,the number of stages needed to perform all tests and the decoding complexity.An asymptotically optimal 2-stage algorithm based on selectors is also given.

In [B29] a new variant of combinatorial group testing, called complete grouptesting problem is introduced: the number of defectives among N items is un-known and one tries to minimize the worst case number of tests needed if therehappen to be at most D defectives. However, the case of more than D defectivesis not excluded, and if more than D defectives are actually present, this must bedetected as well and reported. The author proves that the optimal algorithm forthe complete group testing problem needs exactly one additional test comparedto the optimal algorithm for the basic model.

In [B30] a survey of results on randomized post-optimization for t-restrictionsis given. These constructions can be used for many search problems, also forgroup testing algorithms.

The theory of screening experimental design (SED) can be located in appliedmathematics in the border region of search and information theory ([I08]). Itcomprises models of so-called discrete search problems with randomly disturbedtests; these problems are equivalent to certain coding problems from informationtheory. In particular coding theory for so-called multiple-access channels findsapplication in practical problems here for the first time.

In many “processes” which are dependent on a large number of factors, it isnatural, that one assumes a small number of “meaningful” factors, which reallycontrol the process, and considers the influence of the other factors as mere“experiment errors”. Experiments to identify the meaningful factors are calledselecting experiments.

In the middle of the seventies Mikhail Maljutov published a series of papersabout special models that cleared up the connection to information theory ([I06],

XXII Introduction

[I05]). In [B31] Mikhail Maljutov gives a survey of the known results in SEDfocussing on the relations with the new flourishing area of compressed sensing.

Ahlswede was the first outstanding Western researcher to recognize the re-sults of Maljutov. He endorsed its description in the Addendum to the Russiantranslation of his book “Search Problems”. Ahlswede’s diploma student JochenViemeister at Bielefeld University prepared a detailed survey 45 of results onMaljutov’s results spanning around 200 pages in 1982.

Rudolf Ahlswede became interested in Combinatorics in the early seventies.After a short visit in Budapest he invited Gyula Katona to Gottingen. Their 6month long joint work in 1974 there resulted in two joint papers. This was thebeginning of Ahlswede’s long and bright journey in the field of Combinatorics.They have not written any more joint papers, but they met many times in Biele-feld and Budapest and their cooperation in Combinatorics and Search Theorycontinued in a less intensive way as it can be traced in their publications.

In [B32] Gyula Katona and Krisztian Tichler consider an interesting combi-natorial search problem with errors. In their model, the errors depend on thetarget in the following sense: every permitted question specifies two sets of ele-ments B and a A ⊂ B with |A| ≥ a, where a is a parameter of the problem. Theset A defines the border of reliability of the test, in the sense that if the objectto be found is in A, then the answer can be arbitrarily YES or NO. The authorsgive optimal algorithms for the adaptive and for the non-adaptive case.

For the adaptive case, bounds on the size of the smallest size strategies hadbeen previously given by Ahlswede in [A220].

In [B33] Christian Deppe and Christian Wischmann consider the1-dimensional cutting problem, a search/optimization problem consisting in min-imizing the cost of sawing steel tubes to lengths requested by customers startingfrom longer tubes. The solution given in this paper improves upon the previousresults of Gilmore and Gomory.

To find an (approximately) optimal choice of batches, the graph theoreticalproblem of finding a minimal weighted partition for a weighted hypergraph isused. This is done by interpreting the lengths requested by customers as verticesand every possibility of combining customer’s lengths to a batch as an edge. Theweights of an edge correspond to the minimal cost which arise from combiningall nodes on the edge into one initial length.

The authors show both how to calculate the edge weights, i.e. the minimalcost which arise from combining all nodes into one initial length by using Gilmoreand Gomory’s method, and how to faster calculate the (approximately) minimalcost by using a heuristic method for the knapsack problem. Furthermore, theyderive a heuristic algorithm for the minimal weighted partition of a weightedhypergraph.

Tree search is one of the central algorithms of any game playing program.[B34] is an overview by Ingo Althofer of the evolution of research on the topicof game tree search. The paper provides a succinct overview of the topic ofgame tree search, running all the way from Zermelo at the beginning of the 20thcentury to the present day. For the specialist in the early history of game theory,

Introduction XXIII

it provides useful informations and an overview of the central approaches andconcepts in the development of computer-play of chess and Go.

Rudolf Ahlswede was Ingo Althofer’s teacher at Bielefeld University from1983 to 1993. In his Ackknowledgement he describes how happy he was aboutthe tolerant and unaffected research style of Rudolf Ahlswede. Ingo Althofer in-troduced several students to do computer supported mathematics. Among themwas Bernhard Balkenhol who initated a group working in data compression.Furthermore together with Ahlswede and Khachatrian he formulated the 3/4-conjecture for fix-free codes in 1996. This conjecture is still open and attracts alot of papers.

A fix-free code is a code, which is prefix-free and suffix-free, i.e. any codewordof a fix-free code is neither a prefix, nor a suffix of another codeword. Fix-freecodes were first introduced by Schutzenberger (1956) and Gilbert and Moore(1959), where they were called never-self-synchronizing codes. [B35] establishesa collection of results regarding fix-free codes, i.e., variable length binary codewhere no codeword is either a prefix or a suffix of any other codeword. In par-ticular the author shows that in any fix free code of Kraft sum 2/3 or less one ofthe shorter words can be replaced by a large number of longer words preservingboth the fix free property and the Kraft sum. The author also presents somenew families of complete thin fix free codes.

In [A61] and [A64] Ahlswede, Ye, and Zhang started a new area of researchon creating order in sequence spaces with simple machines. On a very high levelit was to understand how much “order” can be created in a “system” underconstraints on the “knowledge about the system” and on the “actions which canbe performed in the system”. Rudolf Ahlswede was disappointed that this didnot receive much attention. He pointed this out also during his Shannon Lecture.

In [B36]a “multi-user version” is discussed. Here, the output sequence is nolonger a permutation of the input sequence, rather it is a permutation of aselected subsequence of the input sequence. The word of multi-user may not beprecise for the problem studied, rather it is borrowed from multi-user informationtheory. The model studies a case that the rate of input is higher than the rate ofoutput. Another major difference between this model and the original model isthe measurement of the “efficiency” for a particular organization method. It nolonger uses the entropy or cardinality of the output space, it uses the expectedvalue of the time of getting the first 0. Although the model is quite different, itis an interesting mathematical model. Its solution is non-trivial and is relatedto other interesting mathematical problems. Like for the original creating ordermodel, many variations of the model exist which are of interest.

Obituaries and Personal Memories

We refer to the prefaces of [I01] and [A246] for many biographical informationon Rudolf Ahswede. These books appeared on the occasion of Ahlswede’s 60thand six years later on the occasion of Ahlswede’s ZiF Project “General Theoryof Information Transfer and Combinatorics”. In this part of the present volume

XXIV Introduction

we have collected obituaries written by Ahlswede’s family and friends, his super-visor Konrad Jacobs, students and coauthors. We have also included some niceanecdotes. Rudolf Ahlswede liked to tell jokes and laugh about himself and hismischance. It was typical of him to interrupt a lecture to tell a funny story, ahabit which was very much appreciated by his students.

It is not very easy to translate into written form such anecdotes with theiremotional content, however we hope that these stories will help the reader to getyet another glimpse on Rudi’s character and life.

November 2012 Ingo Althofer, Harout Aydinian, Holger Boche,Ning Cai, Ferdinando Cicalese, Christian Deppe,

Vladimir Lebedev, Ulrich Tamm

References

[I01] Althofer, I., Cai, N., Dueck, G., Khachatrian, L.H., Pinsker, M., Sarkozy, A.,Wegener, I., Zhang, Z. (eds.): Numbers, Information and Complexity, Specialvolume in honour of R. Ahlswede on occasion of his 60th birthday. Kluwer Acad.Publ., Boston (2000)

[I02] Damaschke, P.: Threshold Group Testing. In: Ahlswede, R., Baumer, L., Cai, N.,Aydinian, H., Blinovsky, V., Deppe, C., Mashurian, H. (eds.) General Theory ofInformation Transfer and Combinatorics. LNCS, vol. 4123, pp. 707–718. Springer,Heidelberg (2006)

[I03] Effros, M., Kotter, R., Medard, M.: Breaking network logjams. Scientific Ameri-can 296, 78–85 (2007)

[I04] Kilian, J.: Founding cryptography on oblivious transfer. In: Proc. STOC 1988,pp. 20–31 (1988)

[I05] Malyutov, M.B., Mateev, P.S.: Screening designs for non-symmetric responsefunction. Mat. Zametki 27, 109–127 (1980)

[I06] Malyutov, M.B.: On the maximal rate of screening designs. Theory Probab. andAppl. 24, 655–657 (1979)

[I07] Shannon, C.E.: Mathematical theory of communication. Bell Syst. Techn. Jour-nal 27, 339–425, 623–656 (1948)

[I08] Viemeister, J.: Die Theorie selektierender Versuche und MAC, Diplomarbeit.Fakultat fur Mathematik. Universitat Bielefeld (1982)

Search Methodologies I

organized by Rudolf Ahlswede, Ferdinando Cicalese, and Ugo VaccaroDagstuhl, 05.07.09–10.07.09

The main purpose of this seminar was to provide a common forum for researchersinterested in the mathematical, algorithmic, and practical aspects of the prob-lem of efficient searching, as seen in its polymorphic incarnation in the areasof computer science, communication, bioinformatics, information theory, and re-lated fields of the applied sciences. We believe that only the on site collaborationof a variety of established and young researchers engaged in different aspects ofsearch theory might provide the necessary humus for the identification of the ba-sic search problems at the conceptual underpinnings of the new scientific issuesin the above mentioned areas.

Ingo Althofer Monte Carlo Search in Trees and Game TreesHarout Aydinian On Error-Tolerant Pooling Designs Based on

Vector SpacesCharles Colbourn Locating an Interaction FaultPeter Damaschke Competitive Group Testing and Learning

Hidden Vertex Covers with MinimumAdaptivity

Christian Deppe Adaptive Coding Strategies and the Countingof Sequences with Forbidden Pattern

Travis Gagie Minimax Trees in Linear Time withApplications

Mordecai Golin A Generic Top-Down Dynamic-ProgrammingApproach to Prefix-Free Coding

Gyula O.H. Katona Finding at Least One Defective Element inTwo Rounds

Kingo Kobayashi Some Aspects of Finite State Channel relatedto Hidden Markov Process

Evangelos Kranakis Memory/Time Tradeoffs for Rendezvous on aRing

Anthony J. Macula Covert Combinatorial DNA Taggant Signaturesfor Authentication, Tracking and Trace-Back

Martin Milanic Competitive Evaluation of Threshold Functionsand Game Trees in the Priced InformationModel

XXVI Introduction

Olgica Milenkovic Iterative Algorithms for Low-Rank MatrixCompletion

Ely Porat The Beauty of Prime Numbers vs the Beautyof the Random

Søren Riis Graph Entropy, Network Coding and GuessingGames

Eberhard Triesch Searching for Defective Edges in Graphs andHypergraphs

Gabor Wiener Rounds in Combinatorial SearchAnatoly Zhigljavsky Existence Theorems for Search Problems with

Lies

The following researchers spoke in the problem session:

Rudolf Ahlswede, Ferdinando Cicalese, Gianluca De Marco, VladimirLebedev, Ugo Vaccaro, and Soren Werth.

Search Methodologies II

organized by Rudolf Ahlswede and Ferdinando CicaleseZiF, Bielefeld, 25.10.10–29.10.10

This workshop was the opening event of the cooperation group “Search Method-ologies” at the ZiF. We were interested in deepening our understanding of searchproblems and we envision that some unifying principles might be disclosed. Atleast we want to analyze methods and techniques of searching, simplify, compareand/or merge them. One day was devoted to these activities.

The opening lecture by Rudolf Ahlswede explained that time seems to bemature for a more systematic understanding with the goal to build general the-ories of search. Harout Aydinian and Vladimir Lebedev helped as fellows in thisendeavor.

Harout Aydinian On Generic Erasure Correcting Sets andRelated Problems

Vladimir Blinovsky Solutions of Some Problems from ExtremalCombinatorics

Huilan Chang Identication and Classication Problems onPooling Designs for Inhibitor ComplexModels

Hong-Bin Chen Pooling Designs with Sensitive and EcientDecoding

Ferdinando Cicalese Superselectors: Efficient Constructions andApplications

Eva Czabarka Full Transversals and Mixed Orthogonal ArraysPeter Damaschke Randomized and Competitive Group Testing in

StagesAnnalisa De Bonis Combinatorial Group Testing for Corruption

Localizing HashingChristian Deppe Threshold and Majority Group TestingArkadii D’yachkov DNA Codes for Additive Stem DistanceDaniel Gerbner Search with Density TestsTobias Jacobs Searching in TreesSampath Kannan Sampling from Constrained Multivariate

DistributionsGyula O. H. Katona Average Length in q-ary Search with Restricted

Sizes of Question SetsBalazs Keszegh Path-Search in a Pyramid and Other GraphsKingo Kobayashi Some Structures of Tower of Hanoi with Four

Pegs

XXVIII Introduction

Elena Konstantinova Search Problems on Cayley GraphsVladimir Lebedev Shadows Under the Word-Subword RelationUlf Lorenz Searching for Solutions of Hard ProblemsAnthony J. Macula Combinatorial Method for Anomaly DetectionMartin Milanic Haplotype Inference and Graphs of Small

SeparabilityEly Porat An Extension of List Disjunct Matrices

that can Correct Errors in Test OutcomesK. Rudiger Reischuk Searching for Hidden InformationSøren Riis A New Max-Flow Min-Cut Theorem for

Information FlowsVyacheslav V. Rykov An Application of Superimposed Coding

Theory to the Multiple Access OR Channeland Two-Stage Group Testing Algorithms

Christian Sohler Streaming Algorithms for the Analysis ofMassive Data Sets

Laszlo Szekely M-part Sperner familiesOlivier Teytaud Monte-Carlo Tree Search: a New Paradigm for

Computational IntelligenceEberhard Triesch A Lower Bound for the Complexity of Mono-

tone Graph PropertiesAnna N. Voronina DNA Codes for Non-Additive Stem Distance

Search Methodologies III

organized by Ferdinando Cicalese and Christian DeppeZiF, Bielefeld, 03.09.12–07.09.12

Search Methodologies III has been the last of three main events organized withinthis cooperation group. In this final workshop, the programme included four ma-jor topics: theory of games and strategic planning, combinatorial group testingand database mining, computational biology and string matching, coding, infor-mation spreading and patrolling on networks. Besides providing an opportunityfor the dissemination of recent results, beyond the border of the restricted com-munity, we pursued cross-fertilization via several RUMP sessions, namely, specialopen problems and discussion sessions where experts of diverse disciplines couldcooperate on the definition of new models, problems or solutions to open prob-lems. Further there were two tutorial talks on communication complexity andquantum computing.

Matthew Aldridge Adaptive Group Testing: a Channel CodingApproach

Ingo Althofer Strange Phenomena in Monte-Carlo Game TreeSearch

Harout Aydinian Quantum Error Correction: An IntroductionVladimir Balakirsky Extracting Signicant Parameters from Noisy

Observations and Their Use forAuthentication

Bernhard Balkenhol Fuzzy Self-Learning SearchMichael Bodewig Completeness and Multiplication of Fix-Free

Codes Regarding Ahlswedes 3/4-ConjectureEva Czabarka k-Dimensional m-Part Sperner Families and

Mixed Orthogonal ArraysPeter Damaschke On Optimal Strict Multistage Group TestingGianluca De Marco Computing Majority with Triple QueriesAndreas Dress Using Suffix Trees for Alignment-Free Sequence

Comparison and Phylogenetic Reconstruc-tion

Arkadii D’yachkov Superimposed Codes and Non-AdaptiveThreshold Group Testing

Leszek A. Gasieniec Communication-Less Agent Location DiscoveryDaniel Gerbner Majority and Plurality ProblemsGyula O. H. Katona When the Lie Depends on the Target

XXX Introduction

Evangelos Kranakis Boundary Patrolling by Mobile AgentsVladimir Lebedev Group Testing with Two DefectivesZsuzsanna Liptak Some Problems and Algorithms in

Non-Standard String MatchingMikhail Malyutov On Connection with Compressed Sensing and

Some Other New Developments in the SearchTheory

Nikita Polyansky Random Coding Bounds on the Rate forNon-Adaptive Threshold Group Testing

Ely Porat Efficient Signature Scheme for Network CodingRudiger Reischuk The Smoothed Competitive Ratio of Online

CachingSøren Riis Search Problems Related to Dispersion, Graph

Entropy and Guessing GamesAtri Rudra Group Testing and Coding TheoryVyacheslav V. Rykov On Superimposed Codes and DesignsLaszlo Szekely Some Constructions for the Diamond ProblemUlrich Tamm Multiparty Communication Complexity of

Vector-Valued and Sum-Type FunctionsOlivier Teytaud Search with Partial InformationEberhard Triesch Upper and Lower Bounds for Competitive

Group TestingGabor Wiener On a Problem of Renyi and Katona

Symposium in Remembrance of

Rudolf Ahlswede

ZiF, Bielefeld, 25.07.11–26.07.11

Organizers:Harout Aydinian Ingo Althofer Ning CaiFerdinando Cicalese Christian Deppe Gunter DueckUlrich Tamm Andreas Winter

On July 25 and 26 a memorial symposium for Rudolf Ahlswede took place inthe Center for Interdisciplinary Research (ZIF) at the University of Bielefeld.The symposium was organized by the ZIF in close cooperation with RudolfAhlswede’s former students and partners of his many research projects. About100 participants came to Bielefeld to remember life and work of Rudolf Ahlswedewho had passed away suddenly and unexpectedly on December 18, 2010.

Outside the lecture hall there were a poster wall with pictures and perma-nent video presentations from Rudolf Ahlswede’s Shannon lecture and from thememorial session at the ITA in San Diego. At the conference dinner further videoswere presented by Vladimir Lebedev and Tatiana Dolgova about their last visitin Polle and by Rudiger Reischuk from the conference on Rudolf Ahlswede’s 60thbirthday.

Further participants include among others - just to mention the informationtheorists - Arkadii D’yachkov, Peter Gacs, Te Sun Han, Gerhard Kramer, AydinSezgin, Faina Soloveeva, and Frans Willems.

Before the official start of the symposium, a warm-up lecture by CharlesBennett on “Quantum information” already attracted a lot of interest.

The first day then was devoted to personal memories on Rudolf Ahlswede’slife and academic career.

M. Egelhaaf Commemorative address as representatives of the ZiFE. Emmrich Commemorative address as representative of

the Department of Mathematics of the University ofBielefeld

A. Ahlswede andB. Ahlswede-Loghin Joint life with Rudolf AhlswedeK. Jacobs Rudolf Ahlswede’s time in GottingenE. van der Meulen R. Ahlswede 1970-74J. Daykin R. Ahlwede’s cooperation with David DaykinM. Maljutov R. Ahlswede and search theoryG. Dueck Rudolf Ahlswede 1975-1985

XXXII Introduction

I. Althofer Rudolf Ahlswede 1985-1995U. Tamm R. Ahlswede 1995-2000G. Khachatrian R. Ahlswede’s cooperation with Levon KhachatrianN. Cai My cooperation with R. AhlswedeB. Balkenhol R. Ahlswede and the computerK. Kobayashi R. Ahlswede’s cooperation with Japanese researchersV. Blinovsky R. Ahlswede’s cooperation with Russian researchersC. Deppe R. Ahlswede 2000-2010A. Winter R. Ahlswede and quantum information theoryH. Aydinian My cooperation with R. AhlswedeC. Heup The identification of the lucky-dog-entropyF. Cicalese My projects with R. AhlswedeH. Boche R. Ahlswede in Berlin

The second day of the symposium was devoted to scientific lectures onAhlswede’s fields of research.

I. Csiszar Common randomness in information theoryP. Narayan Common randomness and multiterminal secure computationA. Winter Quantum channels and identification theoryA. Sarkozy On the complexity of families of binary sequences and latticesA. Orlitsky String reconstruction from substring compositionsR. Reischuk Stochastic search for locally clustered targetsG. Katona The deep impact of Rudolf Ahlswede on combinatoricsH. Aydinian AZ-identity for regular posetsN. Cai Secure network codingS. Riis Information flows and bottle necks in dynamic communication

networksL. Tolhuizen A generalisation of the Gilbert-Varshamov bound and its

asymptotic evaluationL. Szekely Higher order extremal problemsS. Bezrukov Local-global principles in discrete extremal problems

Introduction XXXIII

Participants: H. Abels, A. Ahlswede, B. Ahlswede (Bielefeld), M. Ahlert (Halle

a.d.Saale), I. Althofer (Jena), H. Aydinian (Bielefeld), A. Bak (Bielefeld), B. Balken-

hol (Bielefeld), C. Bennett (New York, USA), S. Bezrukov (Wisconsin, USA), I. Bje-

lakovic (Munchen), P. Blanchard (Bielefeld), V. Blinovsky (Moscow, RUS), H. Boche

(Munchen), G. Brinkmann (Gent, BE), J. Bultermann (Gutersloh), M. Cai (Bielefeld),

N. Cai (Xian, China), H.-G. Carstens (Bielefeld) F. Cicalese (Salerno, I), I. Csiszar

(Budapest, H), A. D’yachkov (Moscow, RUS), J. Daykin (London, UK), C. Deppe,

E. Diemann (Bielefeld), T. Dolgova (Moscow, RUS), A. Dress (Bielefeld), G. Dueck

(Mannheim), P. Eichelsbacher (Bochum), E. Emmrich (Bielefeld), P. Gacs (Boston,

USA), L. Galumyan, F. Gotze, T. Grotendiek (Heilbronn), O. Gutjahr (Bielefeld),

Te Sun Han (Tokyo, J), C. Heup (Grafschaft), A. Hilton (Reading, UK), W. Hoff-

mann (Bielefeld), K. Jacobs (Bamberg), G. Janßen (Munchen), N. Kalus (Berlin),

G. Katona (Budapest, H), A. Khachatrian (Bielefeld), G. Khachatrian (Yerevan,

Armenia), C. Kleinewachter (Bielefeld), K. Kobayashi (Tokyo, J), K.-U. Koschnick

(Dreieich), G. Kramer (Munchen), H. Krause (Bielefeld), U. Krengel (Gottingen), G.

Kyureghyan (Magdeburg), M. Kyureghyan (Eschborn), V. Lebedev (Moscow, RUS), H.

Lefmann (Chemnitz), Z. Liptak (Salerno, I), P. Lober (Langen), M. Lowe (Munster),

M. Malioutov (Boston, USA), M. Matz (Bielefeld), P. Narayan (Maryland, USA), J.

Notzel (Munchen), J. Obbelode (Gutersloh), A. Orlitsky (San Diego, USA), T. Partner,

C. Petersen, D. Poguntke, U. Rehmann (Bielefeld), K.R. Reischuk (Lubbeck), R. Reis-

chuk (Bielefeld), S. Riis (London, UK), M. Rudolf (Halle), A. Sarkozy (Budapest, H),

A. Sezgin (Bochum), F. I. Solovyeva (Novosibirsk, RUS), N. Spenst (Kirchlengern), E.

Steffen (Paderborn), H. Steidl (Bielefeld), L. A. Szekely (Columbia, USA), U. Tamm

(Istanbul, T), L. Tolhuizen (Eindhoven, NL), E. Van der Meulen (Leuven, Be), D.

Voigt, H.M. Wallmeier, C. Wegener-Murbe, W. Wenzel (Kassel), F. Willems (Eind-

hoven, NL), A. Winter (Bristol, UK)

XXXIV Introduction

Introduction XXXV

L. Khachatrian, P. Erdos, R. Ahlswede(Bielefeld 1995, check of Erdos for the

solution of the 4m-Conjecture)

R. Ahlswede, D.L. Neuhoff (Seattle 2006,Shannon Award)

C. Deppe, A. Ahlswede, R. Ahlswede, and H. Aydinian (Seattle 2006)

Table of Contents

I. Information Theory

1 Two New Results for Identification for Sources . . . . . . . . . . . . . . . . . . . 1Christian Heup

2 L-Identification for Uniformly Distributed Sources and the q-aryIdentification Entropy of Second Order . . . . . . . . . . . . . . . . . . . . . . . . . 11

Christian Heup

3 Optimal Rate Region of Two-Hop Multiple Access Channel viaAmplify-and-Forward Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Binyue Liu and Ning Cai

4 Strong Secrecy for Multiple Access Channels . . . . . . . . . . . . . . . . . . . . 71Moritz Wiese and Holger Boche

5 Capacity Results for Arbitrarily Varying Wiretap Channels . . . . . . . 123Igor Bjelakovic, Holger Boche, and Jochen Sommerfeld

6 On Oblivious Transfer Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Rudolf Ahlswede and Imre Csiszar

7 Achieving Net Feedback Gain in the Linear-Deterministic ButterflyNetwork with a Full-Duplex Relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Anas Chaaban, Aydin Sezgin, and Daniela Tuninetti

8 Uniformly Generating Origin Destination Tables . . . . . . . . . . . . . . . . . 209David M. Einstein and Lee K. Jones

9 Identification via Quantum Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Andreas Winter

10 Classical-Quantum Arbitrarily Varying Wiretap Channel . . . . . . . . . . 234Vladimir Blinovsky and Minglai Cai

11 Arbitrarily Varying and Compound Classical-Quantum Channelsand a Note on Quantum Zero-Error Capacities . . . . . . . . . . . . . . . . . . 247

Igor Bjelakovic, Holger Boche, Gisbert Janßen, and Janis Notzel

12 On the Value of Multiple Read/Write Streams for Data Compression 284Travis Gagie

13 How to Read a Randomly Mixed Up Message . . . . . . . . . . . . . . . . . . . 298Matthias Lowe

XXXVIII Table of Contents

14 Multiple Objects: Error Exponents in Hypotheses Testing andIdentification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Evgueni Haroutunian and Parandzem Hakobyan

II. Combinatorics

15 Family Complexity and VC-Dimension . . . . . . . . . . . . . . . . . . . . . . . . . 346Christian Mauduit and Andras Sarkozy

16 The Restricted Word Shadow Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 364Rudolf Ahlswede and Vladimir Lebedev

17 Mixed Orthogonal Arrays, k-Dimensional M-Part SpernerMultifamilies, and Full Multitransversals . . . . . . . . . . . . . . . . . . . . . . . . 371

Harout Aydinian, Eva Czabarka, and Laszlo A. Szekely

18 Generic Algorithms for Factoring Strings . . . . . . . . . . . . . . . . . . . . . . . . 402David E. Daykin, Jacqueline W. Daykin, Costas S. Iliopoulos,and W.F. Smyth

19 On Data Recovery in Distributed Databases . . . . . . . . . . . . . . . . . . . . . 419Sergei L. Bezrukov, Uwe Leck, and Victor P. Piotrowski

20 An Unstable Hypergraph Problem with a Unique Optimal Solution 432Carlos Hoppen, Yoshiharu Kohayakawa, and Hanno Lefmann

21 Multiparty Communication Complexity of Vector–Valued andSum–Type Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Ulrich Tamm

22 Threshold Functions for Distinct Parts: Revisiting Erdos–Lehner . . . 463Eva Czabarka, Matteo Marsili, and Laszlo A. Szekely

23 On Some Structural Properties of Star and Pancake Graphs . . . . . . . 472Elena Konstantinova

III. Search Theory

24 Threshold and Majority Group Testing . . . . . . . . . . . . . . . . . . . . . . . . . 488Rudolf Ahlswede, Christian Deppe, and Vladimir Lebedev

25 Superimposed Codes and Threshold Group Testing . . . . . . . . . . . . . . . 509Arkadii D’yachkov, Vyacheslav Rykov, Christian Deppe, andVladimir Lebedev

26 New Construction of Error-Tolerant Pooling Designs . . . . . . . . . . . . . 534Rudolf Ahlswede and Harout Aydinian

Table of Contents XXXIX

27 Density-Based Group Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543Daniel Gerbner, Balazs Keszegh, Domotor Palvolgyi, andGabor Wiener

28 Group Testing with Multiple Mutually-Obscuring Positives . . . . . . . . 557Hong-Bin Chen and Hung-Lin Fu

29 An Efficient Algorithm for Combinatorial Group Testing . . . . . . . . . . 569Andreas Allemann

30 Randomized Post-optimization for t-Restrictions . . . . . . . . . . . . . . . . . 597Charles J. Colbourn and Peyman Nayeri

31 Search for Sparse Active Inputs: A Review . . . . . . . . . . . . . . . . . . . . . . 609Mikhail Malyutov

32 Search When the Lie Depends on the Target . . . . . . . . . . . . . . . . . . . . 648Gyula O.H. Katona and Krisztian Tichler

33 A Heuristic Solution of a Cutting Problem Using Hypergraphs . . . . . 658Christian Deppe and Christian Wischmann

34 Remarks on History and Presence of Game Tree Searchand Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677

Ingo Althofer

35 Multiplied Complete Fix-Free Codes and Shiftings Regarding the3/4-Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694

Michael Bodewig

36 Creating Order and Ballot Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 711Ulrich Tamm

Obituaries and Personal Memories

37 Abschied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725Alexander Ahlswede

38 Rudi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726Beatrix Ahlswede Loghin

39 Gedenkworte fur Rudolf Ahlswede . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730Konrad Jacobs

40 In Memoriam Rudolf Ahlswede 1938 - 2010 . . . . . . . . . . . . . . . . . . . . . . 732Imre Csiszar, Ning Cai, Kingo Kobayashi, and Ulrich Tamm

41 Rudolf Ahlswede 1938-2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735Christian Deppe

XL Table of Contents

42 Remembering Rudolf Ahlswede . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739Vladimir Blinovsky

43 Rudi Ahlswede . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741Jacqueline W. Daykin

44 The Happy Connection between Rudi and Japanese Researchers . . . 743Kingo Kobayashi and Te Sun Han

45 From Information Theory to Extremal Combinatorics: My JointWorks with Rudi Ahlswede . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746

Zhen Zhang

46 Mr. Schimanski and the Pragmatic Dean . . . . . . . . . . . . . . . . . . . . . . . . 749Ingo Althofer

47 Broken Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751Thomas M. Cover

48 Rudolf Ahlswede’s Funny Character . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752Ilya Dumer

49 Two Anecdotes of Rudolf Ahlswede . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754Ulrich Tamm

Bibliography of Rudolf Ahlswede’s Publications . . . . . . . . . . . . . . . . . . . . . . 756

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773