Ev Eval aluati uating ng Re Reac achabi abili lity ty Qu - - PowerPoint PPT Presentation

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Ev Eval aluati uating ng Re Reac achabi abili lity ty Qu Quer erie ies ov over er La Large e Soc ocia ial l Gr Grap aphs Imen en BEN DHI HIA Advisor isors: Talel ABEDESSALEM Mauro SOZIO Tl lcom om ParisTech

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SLIDE 1

Ev Eval aluati uating ng Re Reac achabi abili lity ty Qu Quer erie ies

  • v
  • ver

er La Large e Soc

  • cia

ial l Gr Grap aphs

Evaluating Reachability Queries Over Large Social Graphs

Télé lécom

  • m ParisTech

Talel ABEDESSALEM Imen en BEN DHI HIA Mauro SOZIO Advisor isors:

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Control trol Reachab abil ilit ity Queries ies

  • Reacha

chabili bility ty backbo kbone e disc scovery

  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ong

ngoing

  • ing Wo

Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 3

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 4

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Introductio

  • duction to rea

eachabil bilit ity

 Use cases:

s:

 Priv

ivac acy y policies ies evaluat ation ion  Const strained rained rechabili bilibity ity queries ries evaluatio tion. n.

  • 2 to 3 different labels
  • Distance (up to 4) according to real world scenarios

Evaluating Reachability Queries Over Large Social Graphs

U V

friend friend babysitter babysitter Privacy preference Constrained reachability query

U V

colleague friend friend

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SLIDE 5

 Social networks  Bioinformatics

App pplic ication ations

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page 4 Evaluating Reachability Queries Over Large Social Graphs

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1 2 3 4 6 7 8 5 9 13 10 11 12

?Query(1, a\a\b, 11) Yes ?Query(3, a\a\b, 9) No

  • The problem

em: Given two vertices u and v in a directed graph G, is v reachable from u via a given path?

  • A path is a sequence of constraints on label

l order er and distan tance ce.

Constra rain ined ed Rea eachabil bilit ity Problem lem

a b b a a b d e a e a a f f g a

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page 5 Evaluating Reachability Queries Over Large Social Graphs

c a a b

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page 6

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 8

Naïv ïve e Soluti tions

  • ns

Pre-com

comput pute e and s d store e the e transit itiv ive e closure ure (all pa paths bet etween een all po possib ible le pa pair irs of node des)

  • Then, answer any query in constant time: O(1)
  • What are Space requirements for an n-node graph ? O(n2)

Onlin

ine e Sea earch (BFS FS/DFS FS)

  • Answer query Single Source Shortest Path Algorithm
  • Minimal additional space required: O(

O(n+m)

  • What is the time complexity to answer query? O(

O(n+m)

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SLIDE 9

Challen enge ge

Goal

al: : Fi Find ndin ing a g a c compr prom

  • mis

ise e betw etwee een n tim ime e an and s d spa pace e consum umpt ption ion to answer er rea eachabil bilit ity quer erie ies.

 Fi

Find nd a c a compact pact rep epres esen entat ation ion for the e tran ansit itiv ive e closure: sure:

  • whose size is comparable to the data size
  • that supports connection tests (almost) as fast as the naïve

transitive closure lookup

  • that can be built efficiently for large datasets

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SLIDE 10

Rel elated ed Wo Work

 Two main categori

gories es of approac aches: hes:

  • Using

ng spanning ning structur ures (chains ins and trees)

  • Path-tree (Jin et al. ’08)
  • Label-constraint reachability queries (Jin et al. ‘10)
  • Using

ng 2-hop strategy gy

  • 2-hop labeling (Cohen et al. ‘02)
  • Fast graph pattern matching (Wang et al.‘08)

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SLIDE 11

Shortcomin rtcomings gs

 No

Not distance ance-aware are.

 Constraints

straints on label l order r are not respect pected ed.

 Constraints

straints on node proper ertie ties s are not considered. dered.

 Reach

h a bottlen leneck ck when graphs s are large ge

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 13

Our App pproach

 Evalua

valuatin ting g Access s Contr trol l Reacha habi bility lity Queri ries cons nsist ists s in three ree main n steps: ps:

  • 1. Reachability backbone discovery
  • 2. Two-hop index construction
  • 3. Reachability query evaluation over reachability backbone

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 15

 Remark:

k:

  • Multi-graph (with multiple labels) => a set of single labeled graphs.

 Det

etermini ining ng a subset et of nodes that cover two wo-ho hop p paths. s.

  • Shortest two-hop paths sampling.
  • Determining degree threshold.

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Rea eacha habil bilit ity backbone bone di discove very ry

b g m w1 c a l e h f k i n d e w2

  • p

q

Evaluating Reachability Queries Over Large Social Graphs

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 From

  • m Access Cont

ntrol rol to Reachability hability

 Existing

isting Approac aches hes

 Evaluating

luating Access Control trol Reachab abil ilit ity Queries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 17

 2-Hop

  • p cover is

is a a set of

  • f hops (u,

u,v) ) so that every conn nnected ted pair is is covered red by by 2 2 hops

 For each node x,

, we mainta tain in two sets s of labelings lings (which h are simply mply lists ts of no nodes): s): Lin

in(x)

(x) and nd Lout(x) x)

 u

u can reach v v  Lout

  • ut(u)

(u)  Lin

in(v)

(v) ≠ u w v (Cohe

  • hen

n et et al., SODA 2002)

Main in Ide dea: 2-Hop p Cover er & 2 & 2-Hop p Label elin ing

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page 16 Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 18

2-hop

  • p Cover

ers

 Goal:

l:

  • Find

nd a cover which mini nimize mizes the nu number ber of

  • f cent

nters ers wi

 Proble

  • blem

m is is NP NP-hard ard

  • => Approxima
  • ximatio

tion n is is required ired

 Two main

main ingredie edient nts of

  • f the 2-hop cover algorithm

rithm:

  • Set

t cover algorit rithm hm.

  • Densest

sest subgraph raph algorit rithm hm.

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 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 20

 Reach

chab abili ility comput putation tion via reacha chabi bility lity backb kbone ne

  • Performing two local BFS searches for accessing reachability

backbone

  • Reachability join test

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Answer erin ing quer erie ies

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 21

Outli line

 Intro

troduction duction to Reachabilit bility and Applic icat ations ns

 Existing

isting Approac aches hes

 Evaluating

luating Access Cont ntrol rol Reachabi ability ity Que ueries ies

  • Reachabili

chability ty backb kbone

  • ne discovery
  • very
  • 2-hop

hop index ex const struc ructi tion

  • n
  • An

Answe weri ring ng qu queries es

 Ongoin

  • ing

g Work

page 20

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Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 22

 Algor

gorithm ithm implem mplemen entation tation optimization timization

 Us

Using ng MapRed educe uce:

  • For set cover problem
  • To compute densest bipartite graph

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Ongo goin ing Wo Work

Evaluating Reachability Queries Over Large Social Graphs

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SLIDE 23

Th Thanks ks For

  • r You
  • ur Att

ttention ention!

Querying Ordered Label-constraint Reachability in Large Social Graphs page 22