Transcript 幻灯片 1 - Ma, Shuai

Big Graph Search:
Challenges and Techniques
Shuai Ma
Graphs are everywhere, and quite a few are huge graphs!
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Application Scenarios
Software plagiarism detection [1]
• 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 [2].
– Use graph pattern matching to detect plagiarism.
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Application Scenarios
Recommender systems [3]
• 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
 a node denotes a person labeled
with expertise, and
 an edge indicates recommendation,
e.g., HR1 recommends Bio1, and
AI1 recommends DM1
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Application Scenarios
Transport routing [4]
• 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.
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Application Scenarios
Biological data analysis [5]
• 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 highconfidence human protein interactions
obtained from various public interaction
databases by PIN analysis.
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Outline
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What is graph search?
Graph search, why bother?
Challenges & related techniques
Summary
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What is Graph Search?
What is Graph Search?
A unified definition [6] (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)
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What is Graph Search?
Different semantics of “match” implies different “types” of
graph search, including, but not limited to, the following:
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Shortest paths/distances[4]
Subgraph isomorphism[12]
Graph homomorphism and its extensions[10]
Graph simulation and its extensions[8,9]
Graph keyword search[7]
Neighborhood queries[11]
…
Graph search is a very ‘‘ general’’ concept!
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Graph Search, Why Bother?
The need for a Social Search Engine
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:
Facebook launched “graph search” on 16th January, 2013
Assault on Google, Yelp, and LinkedIn with new graph search;
Yelp was down more than 7%
Graph search is a new paradigm for social computing!
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Graph Search vs. RDBMS [13]
Query：
Find the name of all of
Alberto Pepe's friends.
Step 1: The person.name index -> the identifier of Alberto Pepe. [O(log2n)]
Step 2: The friend.person index -> k friend identifiers.
[O(log2x) : x<<m]
Step 3: The k friend identifiers
[O(k log2n)]
-> k friend names.
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Graph Search vs. RDBMS [13]
Query：
Find the name of all of
Alberto Pepe's friends.
Step 1: The vertex.name index -> the vertex with the name Alberto Pepe. [O(log2n)]
Step 2: The vertex returned
-> the k friend names.
[O(k + x)]
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Social Search vs. Web Search
• key words only vs. Phrases、
short sentences
• (Simple Web) pages vs. Entities
• Lifeless vs. Full of life
• History vs. Future
it’s interesting, and over the last 10 years,
people have been trained on how to use
search engines more effectively.
Keywords & Search In 2013: Interview
With A. Goodman & M. Wagner
International Conference on Application
of Natural Language to Information
Systems (NLDB)
started from 1995
Interesting Coincidence!
SIGMOD + VLDB + ICDE
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Social computing
&
Web 2.0
DB people started working on graphs at around the same time！
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Challenges
Social networks are “big data”
Facebook:
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Volume： 10 x 108 users, 2400 x 108 photos, 104 x 108 page visits
Velocity： 7.9 new users per second, over 60 thousands per day
Variety： text (weibo, blogs) , figures, videos, relationships (topology)
Value：1.5 x 108 dollars in 2007, 3 x 108 dollars in 2008, 6 ~ 7 x 108
dollars in 2009, 10 x 108 dollars in 2010.
• Further, data are often dirty due to data missing and data uncertainty [18, 19]
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.
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Query Techniques for Big Graph Search
R = Q(G)
Query Approximation
Key ideas：For a class Q of queries with a high computational
complexity, find another class Q’ of queries that has a lower
computational complexity with bounded quality loss for query
answering.
approximation
Q(D)
Q’(D)
Challenge: balancing the expressive power and computational complexity!
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Graph Pattern Matching [17]
• Given two directed graphs G1 (pattern graph) and
G2 (data graph),
– decide whether G1 “matches” G2 (Boolean queries);
– identify “subgraphs” of G2 that match G1
• Matching Semantics
– Traditional: Subgraph Isomorphism
– Emerging applications: Graph Simulation and its extensions, etc..
Subgraph Isomorphism
(NP-Complete)
Strong Simulation
approximation
(O(n3))
Shuai Ma, Yang Cao, Wenfei Fan, Jinpeng Huai, and Tianyu Wo. Strong Simulation: Capturing Topology in Graph Pattern
Matching. TODS 2014.
Shuai Ma, Yang Cao, Wenfei Fan, Jinpeng Huai, and Tianyu Wo. Capturing Topology in Graph Pattern Matching. VLDB 2012.
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Subgraph Isomorphism[12]
• Given Pattern graph Q, subgraph Gs of data graph G
– Q matches Gs if there exists a bijective function f: VQ→ VGs such that
 for each node u in Q, u and f(u) have the same label
 An edge (u, u‘) in Q if and only if (f(u), f(u')) is an edge in Gs
– Q matches G, via subgraph isomorphsim, if there is such a subraph 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
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Graph Simulation [9, 21]
• 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(n2))!
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Subgraph Isomorphism
Set up a team to develop a new software product
Graph simulation returns F3, F4 and F5;
Subgraph isomorphism returns empty!
Subgraph isomorphism is too strict for emerging applications
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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)
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Strong Simulation[16,17]
• Subgraph isomorphism
– Goodness
 Keep (strong) structure topology
– Badness
 May return exponential number of matched subgraphs
 Decision problem: NP-complete
 In certain scenarios, too restrictive to find sensible matches
• Graph simulation
– Goodness
 Solvable in quadratic time
– Badness
 Lose structure topology (how much? open question)
 Only return a single matched subgraph
Balance between complexity and the capability to capturing topology!
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Strong Simulation
Disconnected
• Graph simulation loses graph structures
Tree
Long cycle
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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
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Strong Simulation
Subgraph
Isomorphism
Strong
Simulation
Dual
Simulation
Graph
Simulation
Topology preservation and bounded matches
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Data Techniques for Big Graph Search
R = Q(G)
Distributed Processing
Q(D1)
Q(D)
Q(Di)
Q(Dn)
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Distributed Processing
• Real-life graphs are typically way too large:
– Yahoo! web graph: 14 billion nodes
– Facebook: over 1 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
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Distributed Processing
Model of Computation [3]:
• 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)
Shuai Ma, Yang Cao, Jinpeng Huai, and Tianyu Wo. Distributed Graph Pattern Matching. WWW 2012.
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Incremental Evaluation
Q(D + Δ)
incrementation
Q(D) + Q(Δ)
known
G. Ramalingam, Thomas W. Reps: A Categorized Bibliography on Incremental Computation. POPL 1993: 502-510
Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, Yinghui Wu, and Yunpeng Wu. Graph Pattern Matching: From Intractable to
Polynomial Time. VLDB 2010
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Incremental Evaluation
Google Percolator
[20]:
• 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 age of documents in Google search
results by 50%.
It is a terrible waste to compute everything from scratch!
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Data Sampling
Q(D)
sampling
Q(Δ)
• 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.
Michael I. Jordan: Divide-and-conquer and statistical inference for big data. KDD 2012: 4
Wenfei Fan, Floris Geerts, Frank Neven: Making Queries Tractable on Big Data with Preprocessing. VLDB 2013
Weiren Yu, Charu Aggarwal, Shuai Ma, and Haixun Wang. On Anomalous Hotspot Discovery in Graph Streams. ICDM 2013
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Data Compression
Q(D)
compression
Q(D’)
• Query oriented compression generates smaller
graphs from original graphs that preserve the
information relevant to a class of queries.
• Specific compression methods are needed for a
given class of queries, e.g., reachability and
neighbor queries
Wenfei Fan, Jianzhong Li, Xin Wang, Yinghui Wu: Query preserving graph compression. SIGMOD, 2012
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Data Partitioning
partitioning
Q(D)
Q(D1) + … + Q(Dn)
• 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.
G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SISC, 20(1):359–392, 1998.
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Summary
We have introduced graph search: a new paradigm for social computing
We have discussed the history and applications of graph search
We have also briefly discussed the challenges of graph search
We have presented some useful techniques towards solving the problems
A long way to go for big graph search!
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Acknowledgements:
Charu Aggarwal, Yang Cao, Wenfei Fan, Kaiyu Feng, Jinpeng Huai, Jia
Li, Jianxin Li, Jianzhong Li, Xudong Liu, Nan Tang, Haixun Wang, Tianyu
Wo, Yinghui Wu, Weiren Yu, …
Homepage: http://mashuai.buaa.edu.cn
Email: [email protected]
Address: Room G1122,
New Main Building,
Beihang University
Beijing, China
References
[1] Chao Liu, Chen Chen, Jiawei Han and Philip S. Yu, GPLAG: detection of software
plagiarism by program dependence graph analysis. KDD 2006.
[2] 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.
[3] Shuai Ma, Yang Cao, Jinpeng Huai, and Tianyu Wo, Distributed Graph Pattern Matching,
WWW 2012.
[4] Rice, M. and Tsotras, V.J., Graph indexing of road networks for shortest path queries
with label restrictions, VLDB 2010.
[5] David A. Bader and Kamesh Madduri, A graph-theoretic analysis of the human proteininteraction network using multicore parallel algorithms. Parallel Computing 2008.
[6] Shuai Ma, Yang Cao, Tianyu Wo, and Jinpeng Huai, Social Networks and Graph
Matching. Communications of CCF, 2012 (in Chinese).
[7] C. C. Aggarwal and H. Wang. Managing and Mining Graph Data. Springer, 2010.
[8] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Adding Regular
Expressions to Graph Reachability and Pattern Queries. ICDE 2011.
[9] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph Pattern
Matching: From Intractable to Polynomial Time. VLDB 2010.
[10] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph
Homomorphism Revisited for Graph Matching. VLDB 2010.
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References
[11] Hossein Maserrat and Jian Pei, Neighbor query friendly compression of social networks.
KDD 2010.
[12] Brian Gallaghe, Matching structure and semantics: A survey on graph-based pattern
matching. AAAI FS. 2006.
[13] Marko A. Rodriguez, Peter Neubauer: The Graph Traversal Pattern. Graph Data
Management 2011: 29-46
[14] S.Wasserman and K. Faust. Social Network Analysis: Methods and Applications.
Cambridge University Press, 1994.
[15] Mehdi Kargar, Aijun An: Keyword Search in Graphs: Finding r-cliques. In VLDB
Conference, 2011.
[16] Shuai Ma, Yang Cao, Wenfei Fan, Jinpeng Huai, and Tianyu Wo, Capturing Topology in
Graph Pattern Matching. VLDB 2012.
[17] Wenfei Fan, Graph Pattern Matching Revised for Social Network Analysis. ICDT 2012.
[18] Eytan Adar and Christopher Re, Managing Uncertainty in Social Networks, IEEE Data
Eng. Bull., pp.15-22, 30(2), 2007.
[19] Gueorgi Kossinets, Effects of missing data in social networks. Social Networks 28:247268, 2006.
[20] Daniel Peng, Frank Dabek: Large-scale Incremental Processing Using Distributed
Transactions and Notifications. OSDI 2010.
[21] Monika Rauch Henzinger, Thomas A. Henzinger, Peter W. Kopke: Computing
Simulations on Finite and Infinite Graphs. FOCS 1995:
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Thanks!
Short Bio
Dr. Shuai Ma
• 2006~2010
• 2001~2004
University of Edinburgh, UK
Peking University, China
PhD
PhD
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Beihang University, China
Microsoft Research, China
Bell Labs, USA
University of Edinburgh, UK
Full Professor
Visiting Researcher
Summer Consultant
Research Fellow
2011~
2012
2008
2005~2010
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