research-article

Regularities and dynamics in bisimulation reductions of big graphs

Authors:

George H. L. Fletcher,

Paul De Bra, and

Yuqing WuAuthors Info & Claims

GRADES '13: First International Workshop on Graph Data Management Experiences and Systems

June 2013

Article No.: 13, Pages 1 - 6

https://doi.org/10.1145/2484425.2484438

Published: 23 June 2013 Publication History

Abstract

Bisimulation is a basic graph reduction operation, which plays a key role in a wide range of graph analytical applications. While there are many algorithms dedicated to computing bisimulation results, to our knowledge, little work has been done to analyze the results themselves. Since data properties such as skew can greatly influence the performances of data-intensive tasks, the lack of such insight leads to inefficient algorithm and system design.

In this paper we take a close look into various aspects of bisimulation results on big graphs, from both real-world scenarios and synthetic graph generators, with graph size varying from 1 million to 1 billion edges. We make the following observations: (1) A certain degree of regularity exists in real-world graphs' bisimulation results. Specifically, power-law distributions appear in many of the results' properties. (2) Synthetic graphs fail to fulfill one or more of these regularities that are revealed in the real-world graphs. (3) By examining a growing social network graph (Flickr-Grow), we see that the corresponding bisimulation partition relation graph grows as well, but the growth is stable with respect to the original graph.

References

[1]

L. Aceto, A. Ingolfsdottir, and J. Srba. The algorithmics of bisimilarity. In Sangiorgi and Rutten {28}, pages 100--172.

[2]

L. A. Adamic. Zipf, Power-laws, and Pareto - a ranking tutorial. http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html.

[3]

L. A. Adamic, R. M. Lukose, A. R. Puniyani, and B. A. Huberman. Search in power-law networks. Phys. Rev. E, 64:046135, Sep 2001.

[4]

D. A. Bader and K. Madduri. GTgraph: A suite of synthetic graph generators. http://www.cse.psu.edu/~madduri/software/GTgraph/index.html.

[5]

C. Bizer and A. Schultz. The Berlin SPARQL Benchmark. IJSWIS, 5(2):1--24, 2009.

[6]

S. Blom and S. Orzan. A distributed algorithm for strong bisimulation reduction of state spaces. Int J Softw Tools Technol Transfer, 7:74--86, 2005.

Digital Library

[7]

P. Buneman, M. Grohe, and C. Koch. Path queries on compressed XML. In Proc. VLDB, pages 141--152, Berlin, Germany, 2003.

Digital Library

[8]

A. Clauset, C. Shalizi, and M. Newman. Power-law distributions in empirical data. SIAM review, 51(4):661--703, 2009.

Digital Library

[9]

E. D. Demaine. Cache-oblivious algorithms and data structures. Lecture Notes from the EEF Summer School on Massive Data Sets. University of Aarhus, Denmark, June 27--July 1, 2002.

[10]

M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the internet topology. SIGCOMM Comput. Commun. Rev., 29(4):251--262, Aug. 1999.

Digital Library

[11]

W. Fan. Graph pattern matching revised for social network analysis. In Proc. ICDT, pages 8--21, Berlin, Germany, 2012.

Digital Library

[12]

W. Fan, J. Li, X. Wang, and Y. Wu. Query preserving graph compression. In Proc. SIGMOD, pages 157--168, Scottsdale, AZ, USA, 2012.

Digital Library

[13]

G. H. L. Fletcher, D. Van Gucht, Y. Wu, M. Gyssens, S. Brenes, and J. Paredaens. A methodology for coupling fragments of XPath with structural indexes for XML documents. Inf. Syst., 34(7):657--670, 2009.

Digital Library

[14]

O. Hassanzadeh and M. P. Consens. Linked Movie Data Base. In Proc. LDOW, Madrid, Spain, 2009.

[15]

T. Heath and C. Bizer. Linked Data: Evolving the Web into a Global Data Space. Synthesis Lectures on the Semantic Web: Theory and Technology, 1(1):1--136, 2011.

[16]

J. Hellings, G. H. L. Fletcher, and H. Haverkort. Efficient external-memory bisimulation on DAGs. In Proc. SIGMOD, pages 553--564, Scottsdale, AZ, USA, 2012.

Digital Library

[17]

M. R. Henzinger, T. A. Henzinger, and P. W. Kopke. Computing simulations on finite and infinite graphs. In Proc. FOCS, pages 453--462, Washington, DC, USA, 1995.

Digital Library

[18]

K. A. Hua and C. Lee. Handling Data Skew in Multiprocessor Database Computers Using Partition Tuning. In Proc. VLDB, pages 525--535, San Francisco, CA, USA, 1991.

Digital Library

[19]

R. Kaushik, P. Shenoy, P. Bohannon, and E. Gudes. Exploiting local similarity for indexing paths in graph-structured data. In Proc. ICDE, pages 129--140, San Jose, CA, USA, 2002.

Digital Library

[20]

H. Kwak, C. Lee, H. Park, and S. Moon. What is Twitter, a social network or a news media? In Proc. WWW, pages 591--600, New York, NY, USA, 2010.

Digital Library

[21]

Y. Luo, Y. de Lange, G. H. L. Fletcher, P. De Bra, J. Hidders, and Y. Wu. Bisimulation Reduction of Big Graphs on MapReduce. In Proc. BNCOD, Oxford, UK, to appear 2013.

Digital Library

[22]

Y. Luo, G. H. L. Fletcher, J. Hidders, Y. Wu, and P. De Bra. I/O-efficient algorithms for localized bisimulation partition construction and maintenance on massive graphs. CoRR, abs/1210.0748, 2012.

[23]

T. Milo and D. Suciu. Index Structures for Path Expressions. In Proc. ICDT, pages 277--295, Jerusalem, Israel, 1999.

Digital Library

[24]

A. Mislove, H. S. Koppula, K. P. Gummadi, P. Druschel, and B. Bhattacharjee. Growth of the Flickr Social Network. In Proc. WOSN, Seattle, WA, USA, August 2008.

Digital Library

[25]

F. Picalausa, Y. Luo, G. H. L. Fletcher, J. Hidders, and S. Vansummeren. A Structural Approach to Indexing Triples. In Proc. ESWC, pages 406--421, Heraklion, Greece, 2012.

Digital Library

[26]

Y. Raimond, M. B. Sandler, and Q. Mary. A Web of Musical Information. In ISMIR, pages 263--268, Philadelphia, PA, USA, 2008.

[27]

D. Sangiorgi. Origins of bisimulation and coinduction. In Sangiorgi and Rutten {28} pages 1--37.

Digital Library

[28]

D. Sangiorgi and J. Rutten, editors. Advanced Topics in Bisimulation and Coinduction. Cambridge University Press, Cambridge, 2011.

Digital Library

[29]

M. Schmidt, T. Hornung, G. Lausen, and C. Pinkel. SP²Bench: A SPARQL Performance Benchmark. In Proc. ICDE, pages 222--233, Washington, DC, USA, 2009.

Digital Library

[30]

J. Scott. Social network analysis. SAGE Publications Limited, 2012.

Cited By

Rau JRicherby DScherp A(2023)Computing k-Bisimulations for Large Graphs: A Comparison and Efficiency AnalysisGraph Transformation10.1007/978-3-031-36709-0_12(223-242)Online publication date: 12-Jul-2023
https://doi.org/10.1007/978-3-031-36709-0_12
Abriola SBarceló PFigueira DFigueira S(2018)Bisimulations on data graphsJournal of Artificial Intelligence Research10.5555/3241691.324169461:1(171-213)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.5555/3241691.3241694
Bonifati AFletcher GVoigt HYakovets N(2018)Querying GraphsSynthesis Lectures on Data Management10.2200/S00873ED1V01Y201808DTM05110:3(1-184)Online publication date: Oct-2018
https://doi.org/10.2200/S00873ED1V01Y201808DTM051
Show More Cited By

Regularities and dynamics in bisimulation reductions of big graphs
1. Mathematics of computing
  1. Discrete mathematics

Recommendations

Collapsible graphs and reductions of line graphs

A graph G is collapsible if for every even subset X@?V(G), G has a subgraph @C such that G-E(@C) is connected and the set of odd-degree vertices of @C is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the ...
Read More
Bisimulation reduction of big graphs on mapreduce
BNCOD'13: Proceedings of the 29th British National conference on Big Data

Computing the bisimulation partition of a graph is a fundamental problem which plays a key role in a wide range of basic applications. Intuitively, two nodes in a graph are bisimilar if they share basic structural properties such as labeling and ...
Read More
Comparability Graphs Among Cover-Incomparability Graphs
Algorithms and Discrete Applied Mathematics
Abstract
Comparability graphs and cover-incomparability graphs (C-I graphs) are two interesting classes of graphs from posets. Comparability graph of a poset $P = (V, \leq)$ is a graph with vertex set V and two vertices u and v are adjacent in V if u and v are ...
Read More

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

GRADES '13: First International Workshop on Graph Data Management Experiences and Systems

June 2013

101 pages

ISBN:9781450321884

DOI:10.1145/2484425

Conference Chairs:
Peter Boncz
CWI
,
Thomas Neumann
TU Munich

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

SIGMOD: ACM Special Interest Group on Management of Data

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 June 2013

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Research-article

Funding Sources

Conference

SIGMOD/PODS'13

Sponsor:

SIGMOD

SIGMOD/PODS'13: International Conference on Management of Data

June 23, 2013

New York, New York

Acceptance Rates

Overall Acceptance Rate 29 of 61 submissions, 48%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
140
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Rau JRicherby DScherp A(2023)Computing k-Bisimulations for Large Graphs: A Comparison and Efficiency AnalysisGraph Transformation10.1007/978-3-031-36709-0_12(223-242)Online publication date: 12-Jul-2023
https://doi.org/10.1007/978-3-031-36709-0_12
Abriola SBarceló PFigueira DFigueira S(2018)Bisimulations on data graphsJournal of Artificial Intelligence Research10.5555/3241691.324169461:1(171-213)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.5555/3241691.3241694
Bonifati AFletcher GVoigt HYakovets N(2018)Querying GraphsSynthesis Lectures on Data Management10.2200/S00873ED1V01Y201808DTM05110:3(1-184)Online publication date: Oct-2018
https://doi.org/10.2200/S00873ED1V01Y201808DTM051
van Heeswijk WFletcher GPechenizkiy MOssowski S(2016)On structure preserving sampling and approximate partitioning of graphsProceedings of the 31st Annual ACM Symposium on Applied Computing10.1145/2851613.2851650(875-882)Online publication date: 4-Apr-2016
https://dl.acm.org/doi/10.1145/2851613.2851650
Khatchadourian SConsens M(2015)Constructing Bisimulation Summaries on a Multi-Core Graph Processing FrameworkProceedings of the GRADES'1510.1145/2764947.2764955(1-7)Online publication date: 31-May-2015
https://dl.acm.org/doi/10.1145/2764947.2764955
Luo YFletcher GHidders JWu YDe Bra PHe QIyengar ANejdl WPei JRastogi R(2013)External memory K-bisimulation reduction of big graphsProceedings of the 22nd ACM international conference on Information & Knowledge Management10.1145/2505515.2505752(919-928)Online publication date: 27-Oct-2013
https://dl.acm.org/doi/10.1145/2505515.2505752

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents