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Indexing and Searching(File Structures)

Modern Information Retrieval (Chapter 8) With G. Navarro

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File Struces Inverted Files Signatures PAT Trees Sequential Searching Compression

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Inverted Files

Information Retrieval: Data Structures and Algorithms(Chapters 3)

W.B. Frakes and R. Baeza-Yates (Eds.) 1992.

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Inverted Files

Characteristics A word-oriented mechanism based on sorted list of keywords,

with each keyword having links to the documents containing that keyword.

Preprocessing Each document is assigned a list of keywords or attributes. Each keyword (attribute) is associated with relevance weights.

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1. The input text is parsed into a list of words along with theirlocation in the text. (time and storage consuming operation)

2. This list is inverted from a list of terms in location order to a list of terms in alphabetical order.

3. Add term weights, or reorganize or compress the files.

Inversion of Word List

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Inversion of Word List

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Structure and Construction

Structure (split the index into two files) Vocabulary: O(n) according to Heaps’ Law Occurrences : depends on the addressing granularity

Construction The vocabulary is stored in lexicographical order and points

to posting list. Posting file ： the lists of occurrences are stored contiguousl

y

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(document #, frequency)

Dictionary and Postings File

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Vocabulary and Posting File

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Structures used in Inverted Files

Vocabulary Sorted Arrays Hashing Structures Keyword Trees: Tries (digital search trees)

The Search Procedure Vocabulary search Retrieval of occurrences Manipulation of occurrences

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Size of an Inverted File Block addressing

The text is divided in blocks, and the occurrences point to the blocks instead of full inverted indices where exact occurrences are recorded

Small collection Medium collection Large Collection

Granularity (1MB) (200MB) (2GB)

Words 45% 73% 36% 64% 35% 63%

Documents 19% 26% 18% 32% 26% 48%

64K blocks 27% 41% 18% 32% 5% 0%

256K blocks 18% 25% 1.70% 2.40% 0.50% 0.70%

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Cost

Advantage easy to implement

Disadvantage updating the index is expensive

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Signature Files

Information Retrieval: Data Structures and Algorithms (Chapters 4)

W.B. Frakes and R. Baeza-Yates (Eds.) Englewood Cliffs, NJ: Prentice Hall, 1992.

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Signature Files

Characteristics Word-oriented index structures based on hashing Low overhead (10%~20% over the text size) at the cost

of forcing a sequential search over the index Suitable for not very large texts Inverted files outperform signature files for most

applications

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Construction and Search

Word-oriented index structures base on hashing Maps words to bit masks of B bits Divides the text in blocks of b words each The mask is obtained by bitwise ORing the signatures of all th

e words in the text block. Search

Hash the query to a bit mask W If W & Bi = W, the text block may contain the word

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Example Four blocks:

This is a text. A text has many words. Words are made from letters. 000101 110101 100100 101101

Hash(text) = 000101 Hash(many)= 110000 Hash(words)= 100100 Hash(made)= 001100 Hash(letters)= 100001

Block 4: 001100 OR 100001

101101

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False Drop

Assumes that m bits are randomly set in the mask Let =m/B For b words, the probability that a given bit of the ma

sk is set is 1-(1-1/B)bm 1-e-b

Hence, the probability that the l random bits are also set is Fd =(1-e-b)False alarm

Fd is minimized for =ln(2)/b Fd = 2-m

m = B ln2/b

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Assume documents span exactly one logical block the size of document signature F = the size of block signature B

Sequential Signature File (SSF)

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Classification of Signature-Based Methods

Horizontal partitioningGrouping similar signatures together and/or providing an index on the signature matrix may result in better-than-linear search.

Vertical partitioningStoring the signature matrix column-wise improves the response time on the expense of insertion time.

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Classification of Signature-Based Methods

Vertical partitioning without compression

bit-sliced signature files (BSSF, B’SSF)frame sliced (FSSF)generalized frame-sliced (GFSSF)

with compressioncompressed bit slices (CBS)doubly compressed bit slices (DCBS)no-false-drop method (NFD)

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Classification of Signature-Based Methods

Sequential storage of the signature matrix without compression

sequential signature files (SSF) with compression

bit-block compression (BC)variable bit-block compression (VBC)

Horizontal partitioning data independent partitioning

Gustafson’s methodpartitioned signature files

data dependent partitioning2-level signature files5-trees

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Criteria

The storage overhead The response time on single word queries The performance on insertion, as well as whether

the insertion maintains the “append-only” property

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Vertical Partitioning

Ideaavoid bringing useless portions of the document signature in main memory

Methods store the signature file in a bit-sliced form or in a frame-

sliced form store the signature matrix column-wise to improve the

response time on the expense of insertion time

Bit-Sliced Signature Files (BSSF)

Transposed bit matrix

transpose

represent

documents

documents(document signature)

F bit-files

search: (1) retrieve m bit-files. e.g., the word signature of free is 001 000 110 010 the document contains “free”: 3rd, 7th, 8th, 11th bit are set i.e., only 3rd, 7th, 8th, 11th files are examined. (2) “and” these vectors. The 1s in the result N-bit vector

denote the qualifying logical blocks (documents).(3) retrieve text file through pointer file.

insertion: require F disk accesses for a new logical block (document), one for each bit-file, but no rewriting

documents

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Frame-Sliced Signature File (FSSF)

Ideas Random disk accesses are more expensive than sequential

ones Force each word to hash into bit positions that are closer to

each other in the document signature these bit files are stored together and can be retrieved with a

few random accesses Procedures

The document signature (F bits long) is divided into k frames of s consecutive bits each.

For each word in the document, one of the k frames will be chosen by a hash function.

Using another hash function, the word sets m bits in that frame.

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documents

frames

Each frame will be kept in consecutive disk blocks.

Frame-Sliced Signature File (Cont.)

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FSSF (Continued)

Example (n=2, B=12, s=6, f=2, m=3)Word Signaturefree 000000 110010text 010110 000000

doc. signature 010110 110010 Search

Only one frame has to be retrieved for a single word query. I.E., only one random disk access is required.e.g., search documents that contain the word “free”->because the word signature of “free” is placed in 2nd frame,only the 2nd frame has to be examined.

At most k frames have to be scanned for an k word query. Insertion

Only f frames have to be accessed instead of F bit-slices.

Horizontal Partitioning

documents

1. Goal: group the signatures into sets, partitioning the signature matrix horizontally.2. Grouping criterion

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Partitioned Signature Files

Using a portion of a document signature as a signature key to partition the signature file.

All signatures with the same key will be grouped into a so-called “module”.

When a query signature arrives, examine its signature key and look for the

corresponding modules scan all the signatures within those modules that have

been selected

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Suffix Trees

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Suffix Trees and Suffix Arrays

Each position in the text is considered as a text suffix

Index points are selected form the text, which point to the beginning of the text positions which will be retrievable

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Suffix arrays

The main drawbacks of Suffix Array are its costly construction process.

Allow binary searches done by comparing the contents of each pointer.

Supra-indices (for large suffix array)

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Construction of Suffix Arrays for Large Texts

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Sequential Searching

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Algorithms

Brute Force Knuth-Morris-Pratt Boyer-Moore Family Shift-Or Suffix Automaton

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Knuth-Morris-Pratt

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Boyer-Moore Family

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Shift-Or

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Suffix Automaton

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Pattern Matching

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Algorithms

Searching allowing errors Dynamic Programming Automaton

Regular Expressions and Extended patterns Pattern Matching Using Indices

Inverted files Suffix Trees and Suffix Arrays

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Dynamic Programming

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Automaton

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Regular Expressions

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Pattern Matching Using Indices Inverted Files

The types of queries such as suffix or substring queries, searching allowing errors and regular expressions, are solved by a sequential search

The restriction is to find approximate matches or regular expressions that span many word.

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Pattern Matching Using Indices

Suffix Trees Suffix trees are able to perform complex searches

• Word, prefix, suffix, substring, and Range queries• Regular expressions• Unrestricted approximate string matching

Useful in specific areas• Find the longest substring• Find the most common substring of a fixed size

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Pattern Matching Using Indices

Suffix Arrays Some patterns can be searched directly in the suffix array wi

thout simulation the suffix tree Word, prefix, suffix, subword search and range search

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Compression

Compressed text--Huffman coding Taking words as symbols Use an alphabet of bytes instead of bits

Compressed indices Inverted Files Suffix Trees and Suffix Arrays Signature Files