Achieving fast (approximate) event matching in large-scale content- based publish/subscribe networks Yaxiong 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 networks Pub/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 subscription Title = {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 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] subscription 1 – 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 Attributes levels cell IDs Subscription 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 10 8 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

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