Achieving fast (approximate) event matching in large-scale content-

based publish/subscribe networksYaxiong Zhao and Jie Wu

The speaker will be graduating next summer

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Content-based pub/sub networksPub/sub provides hustle-free messaging between users

Content-based pub/sub (CBPS) provides yet more expressiveness

Subscription

Message

Pub/sub routing

Content representation model: how to describe contents?• Boolean expression model• Attribute constraints: a primitive description

of the constraints on a attribute’s value• A subscription/filter is defined as a

conjunction of multiple attribute constraints• Each message has multiple attribute

assignments conference = ICDCS ᴧ keywords {content, pub, sub}∈

Title = {xyz} ᴧ conference = ICDCS ᴧ keywords = {content}

Preliminary: counting algorithm

• Since each subscription is a conjunctive form of multiple attribute constraints– A message matches a subscription i.f.f. it matches

all attribute constraints of the subscription– Counting algorithm works by counting the number

of matched attribute constraints– Matches if the number is equal to the number of

all the attribute constraints of the subscriptionTitle = {xyz} ᴧ conference = ICDCS ᴧ keywords = {content}

conference = ICDCS ᴧ keywords {content, pub, sub}∈

Matches 2 attribute constraints so it matches the subscription

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Dissecting the counting algorithm

• The algorithm goes through two steps– Retrieving matched attribute constraints• The most time consuming stage• The focus of this paper

– Comparing the number of matched constraints with the number of constraints for each subscription and return matched subscription• It’s possible to shortcut this process

Optimizing the retrieval stage

• The naïve approach, i.e. examining all attribute constraints, only works for very small amount– A few thousand

• More intelligent techniques– Binary search to eliminate unmatched constraints• SIENA (Sigcomm’03)

– Clustering possibly-matched constraints• Faster matching (Sigmod’01)

Range-based attribute constraints• Range-based attribute constraints represent an

cell that an attribute’s value should be in– Can be seen as a conjunction of two primitive

attribute constraints

• General enough to replace primitive attribute constraints– A primitive constraint can be translated to a range-

based constraint

– Range-based constraints are highly desirable

Height > 100 & Height < 200 Height (100, 200)∈

Height < 200 => Height > 0 & Height < 200

Basic idea

• Reverse indexing of subscriptions– Instead of check each subscription to see what

assignments match it– Directly retrieve the matched attribute constraints

for each attribute assignment

We need a data structure to mapping between attribute value and attribute constraints

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Reverse indexing

• Indexing subscriptions through their represented ranges for each attribute– [100 < height < 200]– [100, 200] <-> subscription1

– Given an assignment “height = 150” we can find all its matched subscriptions by find the ranges containing this value

Discretization• Represent an arbitrary range by evenly separated

cells– Mapping between value and its corresponding cell is fast

• Results in false positive/negative (approximate matching)– We only accept false positives– Guarantee user satisfaction

[0, 1, 2] is used to represent this attribute constraint

Index tree and subscription discretization

• The naïve discretization has a scalability issue– The worst-case false positive is • 2 * cell-length / range-length

– To achieve a false positive of p• The number of cell is 1/p

• An analog is counting numbers– Need exactly “n” tokens to represent the number

“n”

A very simple remedy

• Just like counting in positional notation• Binary separating the attribute value space– Each cell is evenly divided into two in the next

level– Log(1/p) cells– Much better scalability

{level 2 : 1; level 3: 1, 4; level 4 : 1, 10}

Working with counting algorithm

• Each range attribute constraint is discretized on multiple levels– Each cell ID associates with a subscription ID

• Retrieval stage– Table lookup

• Counting stage– Incremental the counters for subscription IDs– Comparing counters’ values to the number of attribute constraints

of subscription

Attributeslevels

cell IDsSubscription IDs

Implementation• Data structure organization– Matching table: for discretized cell ID and subscription ID

mapping

– Subscription ID and attribute constraint counts mapping• Linear table

• More details are in the paper

Dynamic matching for shortcutting matching process

• In many situations we do not need to find all matched subscriptions– Interface matching• Stop matching once any one of the associated

subscription matches• Just examine a fraction of the discretization levels

Optimal binary separation• The above analysis assumes uniform distribution of

the attribute values of events

• The analysis holds for non-uniform distribution only when– Event values are evenly distributed on each cell– I.e. the number of events fall into each cell is the same

• Optimal binary separation does this– Bisecting a range at its median– Ensure that each cell contains the same amount of events

If 90% event’s attribute values fall into here

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Eliminating false positives• Two types: interface false and subscription– Matches a wrong interface– Matches a wrong subscription

• Situations that no false positive occurs– Interface/subscriptions matched before the last

discretization level– Can be used to short-cutting interface matching

• To eliminate false positives– Double check the subscriptions that are matched at

the last discretization level

Outline

• Background– Content-based pub/sub networks– Counting algorithm

• The design– Problem formulation– Index tree based discretization

• Potential improvements• Performance evaluation

Experiment settings

• A working prototype written in C++– As a forwarding component in Siena– Total number of attributes is 1,000– Number of attributes per event 100 – 1,000– Relative width of attribute constraints 0.01 – 0.1

Subscription matching time (degenerate case)

• With of attribute constraints: 0.01 (relative to the entire value space)

• 10 range constraints per subscription

• Each event has 100 attribute assignments

• 3.23ms to return all matched subscription for an event with 20 million attribute constraints– Orders of magnitude faster

than Siena

Interface matching speeding w/ vs w/o shortcutting

• Fix the total number of subscriptions to 20,000

• Vary the number of subscriptions (filters) per interface

• Present the changes of interface matching with two different widths of attribute constraints

Relative value of the width of attribute constraints

Subscription matching FPR• Stores 20,000 subscriptions• Vary the width of attribute

constraints and the number attributes per subscription

• 108 events• Feed 10,000 events to the

matching table

Interface matching FPR• 20,000 subscriptions• 2,000 subscriptions per

interface• Change the width of range

constraints and the number of attributes per subscription

Q&A

Thank you for listening!yaxiong.zhao@temple.eduDrop me an Email if your questions are not answered here