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

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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs

Outli line  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 overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ong ngoing oing Wo Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 1

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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 2

Introductio oduction to rea eachabil bilit ity  Use cases: s: colleague friend friend U V friend friend babysitter babysitter U V Privacy preference Constrained reachability query  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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 3

App pplic ication ations  Social networks  Bioinformatics Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 4

Constra rain ined ed Rea eachabil bilit ity Problem lem  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 . 11 b b g e 13 10 12 ?Query(1, a\a\b, 11) a b a a a Yes a 6 7 8 9 ?Query(3, a\a\b, 9) e c b f a a 3 4 5 No a d f a 1 2 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 5

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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 6

Naïv ïve e Soluti tions ons  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(n 2 )  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) Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 7

Challen enge ge  Goal al: : Fi Find ndin ing a g a c compr prom omis 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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 8

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) Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 9

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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 10

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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 11

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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 12

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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 13

Rea eacha habil bilit ity backbone bone di discove very ry  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. i p e o d m g c w 2 a w 1 n h b q f l e k Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 14

Outli line  Intro troduction duction to Reachabilit bility and Applic icat ations ns  From om 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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 15

Main in Ide dea: 2-Hop p Cover er & 2 & 2-Hop p Label elin ing  2-Hop op cover is is a a set of of 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): L in in (x) (x) and nd L out (x) x) v  L out (u)  L in (v) ≠   u u can reach v out (u) in (v) u w v (Cohe ohen n et et al., SODA 2002) Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 16

2-hop op Cover ers  Goal: l: • Find nd a cover which mini nimize mizes the nu number ber of of cent nters ers w i  Proble oblem m is is NP NP-hard ard • => Approxima oximatio tion n is is required ired  Two main main ingredie edient nts of of the 2-hop cover algorithm rithm: • Set t cover algorit rithm hm. • Densest sest subgraph raph algorit rithm hm. Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 17

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 one discovery overy • 2-hop hop index ex const struc ructi tion on • An Answe weri ring ng qu queries es  Ongoin oing g Work Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 18

Answer erin ing quer erie ies  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 Télé lécom om ParisTech Evaluating Reachability Queries Over Large Social Graphs page 19