Graph Search a New Paradigm for Social Computing

Graph Search: a New Paradigm for Social Computing Shuai Ma

Graphs are everywhere, and quite a few are huge graphs! 2

Graph Search - Why Bother? File systems Databases World Wide Web Social Networks • File systems - 1960’s： very simple search functionalities • Databases - mid 1960’s：SQL language • World Wide Web - 1990’s：keyword search engines • Social networks - late 1990’s: 1. Graphs have more expressive power, compared with RDB & XML. 2. Relationships become important for search – Google Knowledge Graph search is a new paradigm for social computing! 3

Interesting Coincidence! SIGMOD + VLDB + ICDE 40 35 30 25 20 15 10 5 0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Social computing & Web 2. 0 DB people started working on graphs at around the same time！ 4

Outline • • • Application scenarios What is graph search? Three types of graph search Problems and challenges Related techniques Summary 5

Application Scenarios 6

Application Scenarios Complex object identification • Data quality – Real-life data is often dirty: 1%– 5% of business data contains errors – Dirty costs us businesses 600 billion dollars each year – Wrong price data in retail databases alone costs US consumers $2. 5 billion annually – Data cleaning tools deliver an overall business value of more than ‘‘ 600 million GBP’’ each year at BT. • Data cleaning – Data repairing – Record matching (aka. object identification, entity resolution, data deduplication) • Complex object identification – Modeling complex objects as graphs 7

Application Scenarios Software plagiarism detection [13] • Traditional plagiarism detection tools may not be applicable for serious software plagiarism problems. • A new tool based on graph pattern matching – Represent the source codes as program dependence graphs [14]. – Use graph pattern matching to detect plagiarism. 8

Application Scenarios Transport routing [16] • Graph search is a common practice in transportation networks, due to the wide application of Location-Based Services. • Example: Mark, a driver in the U. S. who wants to go from Irvine to Riverside in California. – If Mark wants to reach Riverside by his car in the shortest time, the problem can be expressed as the shortest path problem. Then by using existing methods, we can get the shortest path from Irvine, CA to Riverside, CA traveling along State Route 261. – If Mark drives a truck delivering hazardous materials may not be allowed to cross over some bridges or railroad crossings. This time we can use a pattern graph containing specific route constraints (such as regular expressions) to find the optimal transport routes. 9

Application Scenarios Recommender systems [13] • Recommendations have found its usage in many emerging specific applications, such as social matching systems. • Graph search is a useful tool for recommendations. – A headhunter wants to find a biologist (Bio) to help a group of software engineers (SEs) analyze genetic data. – To do this, (s)he uses an expertise recommendation network G, as depicted in G, where ü a node denotes a person labeled with expertise, and ü an edge indicates recommendation, e. g. , HR 1 recommends Bio 1, and AI 1 10

Application Scenarios Biological data analysis [17] • A large amount of biological data can be represented by graphs, and it is significant to analyze biological data with graph search techniques. – “Protein-interaction network (PIN) analysis provides valuable insight into an organism’s functional organization and evolutionary behavior. ” – For example, one can get the topological properties of a PIN formed by high-confidence human protein interactions obtained from various public interaction databases by PIN analysis. 11

What is Graph Search? 12

What is Graph Search? A unified definition[3] (in the name of graph matching): • Given a pattern graph Gp and a data graph G: – check whether Gp ‘‘matches’’ G; and – identify all ‘‘matched’’ subgraphs. Remarks: – Two classes of queries: – Boolean queries (Yes or No) – Functional queries, which may use Boolean queries as a subroutine – Graphs contain a set of nodes and a set of edges, typically with labels – Pattern graphs are typically small (e. g. , 10), but data graphs are usually huge (e. g. , 108) 13

What is Graph Search? Different semantics of “match” implies different “types” of graph search, including, but not limited to, the following: • • Shortest paths/distances[11] Subgraph isomorphism[12] Graph homomorphism and its extensions[9] Graph simulation and its extensions[7, 8] Graph keyword search[2] Neighborhood queries[10] … Graph search is a very general concept! 14

Three Types of Graph Search • Cohesive subgraphs • Keyword search on graphs • Graph pattern matching 15

Cohesive Subgraphs • Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties [1]. – Different cohesive subgroups are formed according to different cohesive relations, which are further specified by application needs. • Social networks can be represented as graphs, such that we formalize cohesive subgroups as cohesive subgraphs. – Correspondingly, the problem of finding cohesive subgraphs on graphs are referred to as Cohesive subgraph search. 16

Cohesive Subgraphs • Various cohesive subgraphs (clique, n-clan, k-plex, kcore) Maximal clique: a maximal clique is a maximal complete subgraph. • Main issues: – Cliques can overlap – Too many or too few cliques emerge – The problem is NPcomplete “Padgett's Florentine Families” 17

Cohesive Subgraphs • Various cohesive subgraphs (clique, n-clan, k-plex, kcore) N-clique: an n-clique is a maximal subgraph in which the largest distance between any two nodes is no greater than n. N-clan: an n-clan is an n-clique in which the diameter is no greater than n. K-core: a k-core is a maximal subgraph in which the nodal degree of each node is no smaller than k. “Padgett's Florentine Families” The cohesive relations are gradually looser 18

Keyword Search on Graphs • Given a set of keywords and a data graph, the problem is to determine a group of densely linked nodes in the graph such that the nodes together – contain all the keywords, and – satisfy some structural constrains [2] Remarks: 1. Different “structure constraints” implies different types of keyword search. 2. Keyword search is a very simple but user-friendly information retrieval mechanism. 19

Keyword Search on Graphs Given keywords: {A, B} Minimum spanning tree [2] 20

Keyword Search on Graphs r-clique [18] Lack of input structure constrains, the results requires ranking Lack justification of the usage of the structure constrains 21

Graph Pattern Matching • Given two directed graphs G 1 (pattern graph) and G 2 (data graph), – decide whether G 1 “matches” G 2 (Boolean queries); – identify “subgraphs” of G 2 that match G 1 • Matching Semantics – Traditional: Subgraph Isomorphism – Emerging applications: Graph Simulation and its extensions, etc. . 22

Subgraph Isomorphism • Given Pattern graph Q, subgraph Gs of data graph G – Q matches Gs if there exists a bijective function f: VQ→ VGs such that ü for each node u in Q, u and f(u) have the same label ü An edge (u, u‘) in Q if and only if (f(u), f(u')) is an edge in Gs • Goodness: Keep exact structure topology between Q and Gs • Badness: Decision problem is NP-complete May return exponential many matched subgraphs In certain scenarios, too restrictive to find matches These hinder the usability in emerging applications, e. g. , social networks 23

Graph Simulation • Given pattern graph Q(Vq, Eq) and data graph G(V, E), a binary relation R ⊆ Vq × V is said to be a match if – (1) for each (u, v) ∈ R, u and v have the same label; and – (2) for each edge (u, u′) ∈ Eq, there exists an edge (v, v′) in E such that (u′, v′) ∈ R. • Graph G matches pattern Q via graph simulation, if there exists a total match relation M – for each u ∈ Vq, there exists v ∈ V such that (u, v) ∈ M. – Intuitively, simulation preserves the labels and the child relationship of a graph pattern in its match. – Simulation was initially proposed for the analyses of programs; and simulation and its extensions were recently introduced for social networks. Subgraph isomorphism (NP-complete) vs. graph simulation (O(n 2))! 24

Subgraph Isomorphism Set up a team to develop a new software product Graph simulation returns F 3, F 4 and F 5; Subgraph isomorphism returns empty! Subgraph isomorphism is too strict for emerging applications 25

Terrorist Collaboration Network “Those who were trained to fly didn’t know the others. One group of people did not know the other group. ” (Osama Bin Laden, 2001) 26

Strong Simulation[6] • Subgraph isomorphism – Goodness ü Keep (strong) structure topology – Badness ü May return exponential number of matched subgraphs ü Decision problem: NP-complete ü In certain scenarios, too restrictive to find sensible matches • Graph simulation – Goodness ü Solvable in quadratic time – Badness ü Lose structure topology (how much? open question) ü Only return a single matched subgraph Balance between complexity and the capability to capturing topology! 27

Strong Simulation Disconnected • Graph simulation loses graph structures Tree Long cycle 28

Strong Simulation • Duality (dual simulation) – Both child and parent relationships – Simulation considers only child relationships • Locality – Restricting matches within a ball – When social distance increases, the closeness of relationships decreases and the relationships may become irrelevant • The semantics of strong simulation is well defined – The results are unique Strong simulation: bring duality and locality into graph simulation 29

Strong Simulation Subgraph Isomorphism Strong Simulation Dual Simulation Graph Simulation Topology preservation and bounded matches 30

Strong Simulation • A new matching model referred to as strong simulation • A cubic time algorithm • Three main optimization techniques – Query minimization ü An O(n 2) algorithm – Dual simulation filtering ü First compute the match graph of dual simulation, then project on each ball of the data graph – Connectivity pruning ü Based on the connectivity theorem • A distributed algorithm – Data locality property – Boundary nodes and radius Towards revising conventional notions of graph matching 31

Problems and Challenges 32

Problems Analyses: Graph search Userfriendliness Result-accuracy Cohesive Subgraphs Keyword Search Keywords Graph Pattern Matching Pattern graphs Result ranking More accurate (well structure constrained) A novel approach to combining the advantages and overcoming the shortcomings of existing graph search. 33

Challenges Some facts: – Facebook: over 0. 8 billion users, 7. 9 new users increased per second, more than 600 thousand new users increased every day. – Twitter: over 0. 1 billion users, more than 300 thousand new users increased every day. – Data are often dirty due to data missing and data uncertainty [19, 20] 34

Challenges – The amount of data has reached hundred millions orders of magnitude. Graph search with high efficiency, striking a balance between its performance and accuracy. – The data are updated all the time, and the updated amount of data daily reaches hundred thousands orders of magnitude. Consider the dynamic changes and timing characteristics of data. – Same with traditional relational data, there exists data quality problems such as data uncertainty and data missing in the new applications. Solve the data quality problems. 35

Related Techniques 36

Distributed Processing • Real-life graphs are typically way too large: – Yahoo! web graph: 14 billion nodes – Facebook: over 0. 8 billion users It is NOT practical to handle large graphs on single machines • Real-life graphs are naturally distributed: – Google, Yahoo! and Facebook have large-scale data centers Distributed graph processing is inevitable It is nature to study “distributed graph search”! 37

Distributed Processing Model of Computation [15]: • A cluster of identical machines (with one acted as coordinator); • Each machine can directly send arbitrary number of messages to another one; • All machines co-work with each other by local computations and message-passing. Complexity measures: 1. Visit times: the maximum visiting times of a machine (interactions) 2. Makespan: the evaluation completion time (efficiency) 3. Data shipment: the size of the total messages shipped among distinct machines (network band consumption) 38

Incremental Techniques Google Percolator [21]: • Converting the indexing system to an incremental system, • Reduce the average document processing latency by a factor of 100 • Process the same number of documents per day, while reducing the average of documents in Google search results by 50%. It is a great waste to compute everything from scratch! 39

Data Preprocessing • Data sampling – Instead of dealing with the entire data graphs, it reduces the size of data graphs by sampling and allows a certain loss of precision. – In the sampling process, ensure that the sampling data obtained can reflect the characteristics and information of the original data graphs as much as possible. • Data compression – It generates small graphs from original data graphs that preserve the information only relevant to queries. – A specific compression method is applied to a specific query application, such that data graph compression is not universal for all query applications. – Reachability query, Neighbor query 40

Data Preprocessing • Indexing • There are mainly three standards for measuring the goodness of an indexing method. – The space of a graph index – Establishing time for a graph index – Query time with a graph index • Data partitioning – Partition a data graph to relatively “small” graphs – Hash function is a simple approach for random partitioning. – There are well established tools, e. g. Metis. 41

Summary 42

We have introduced graph search: a new paradigm for social computing We have discussed the history and applications of graph search We have introduced analyzed three types of graph search： – Cohesive subgraphs – Keyword search on graphs – Graph pattern matching We have pointed out the problems and challenges We have presented some useful techniques to solve the problems 43

References [1] S. Wasserman and K. Faust. Social Network Analysis: Methods and Applications. Cambridge University Press, 1994. [2] C. C. Aggarwal and H. Wang. Managing and Mining Graph Data. Springer, 2010. [3] Shuai Ma, Yang Cao, Tianyu Wo, and Jinpeng Huai, Social Networks and Graph Matching. Communications of CCF, 2012. [4] Shuai Ma, Jia Li, Xudong Liu, and Jinpeng Huai, Graph Search: A New Searching Approach to the Social Computing Era. Communications of CCF, 2012. . [5] Wenfei Fan, Graph Pattern Matching Revised for Social Network Analysis. ICDT 2012. [6] Shuai Ma, Yang Cao, Wenfei Fan, Jinpeng Huai, and Tianyu Wo, Capturing Topology in Graph Pattern Matching. VLDB 2012. [7] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Adding Regular Expressions to Graph Reachability and Pattern Queries. ICDE 2011. [8] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph Pattern Matching: From Intractable to Polynomial Time. VLDB 2010. [9] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph Homomorphism Revisited for Graph Matching. VLDB 2010. [10] Hossein Maserrat and Jian Pei, Neighbor query friendly compression of social networks. KDD 2010. [11] Rice, M. and Tsotras, V. J. , Graph indexing of road networks for shortest path queries with label restrictions. VLDB 2010. 44

References [12] Brian Gallaghe, Matching structure and semantics: A survey on graph-based pattern matching. AAAI FS. 2006. [13] Chao Liu, Chen, Jiawei Han and Philip S. Yu, GPLAG: detection of software plagiarism by program dependence graph analysis. KDD 2006. [14] J. Ferrante, K. J. Ottenstein, and J. D. Warren. The program dependence graph and its use in optimization. ACM Trans. Program. Lang. Syst. , 9(3): 319– 349, 1987. [15] Shuai Ma, Yang Cao, Jinpeng Huai, and Tianyu Wo, Distributed Graph Pattern Matching, WWW 2012. [16] Rice, M. and Tsotras, V. J. , Graph indexing of road networks for shortest path queries with label restrictions, VLDB 2010. [17] David A. Bader and Kamesh Madduri, A graph-theoretic analysis of the human protein-interaction network using multicore parallel algorithms. Parallel Computing 2008. [18] Mehdi Kargar, Aijun An: Keyword Search in Graphs: Finding r-cliques. In VLDB Conference, 2011. [19] Eytan Adar and Christopher Re, Managing Uncertainty in Social Networks, IEEE Data Eng. Bull. , pp. 15 -22, 30(2), 2007. [20] Gueorgi Kossinets, Effects of missing data in social networks. Social Networks 28: 247 -268, 2006. [21] Daniel Peng, Frank Dabek: Large-scale Incremental Processing Using Distributed Transactions and Notifications. OSDI 2010. 45

Book Recommendation 46

Databases and Logic 47

Computational Complexity 48

Algorithms 49

Formal Languages 50

Statistics and Social Networks 51

Graph Theory 52

Acknowledgement: Yang Cao, Wenfei Fan, Kaiyu Feng, Jinpeng Huai, Jia Li, Jianzhong Li, Xudong Liu, Nan Tang, Tianyu Wo, Yinghui Wu, … Homepage: http: //mashuai. buaa. edu. cn Email: mashuai@buaa. edu. cn Address: Room G 1122, New Main Building, Beihang University 53