Flow-based algorithms for local graph clustering

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2014, Pages 1267-1286

  Orecchia, Lorenzo ^a   Zhu, Zeyuan Allen ^b  

^a MIT Mathematics   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; FLOW GRAPHS; RANDOM PROCESSES;

FLOW BASED ALGORITHMS; GRAPH PARTITIONING; GRAPH PARTITIONING ALGORITHMS; IMPROVEMENT PROBLEMS; INTERNAL CONNECTIVITY; OUTPUT CONDUCTANCE; PARAMETER REGIMES; THEORETICAL GUARANTEES;

CLUSTERING ALGORITHMS;

EID: 84902108776     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973402.94     Document Type: Conference Paper

References (35)

1. Noga Alon. Eigenvalues and expanders. Combinatorica, 6(2):83-96, 1986.
2. L. Alvisi, A. Clement, A. Epasto, S. Lattanzi, and A. Panconesi. The evolution of sybil defense via social networks. In IEEE Symposium on Security and Privacy, 2013.
3. Reid Andersen, Fan Chung, and Kevin Lang. Using pagerank to locally partition a graph. 2006. An extended abstract appeared in FOCS '2006.
4. Reid Andersen, David F. Gleich, and Vahab Mirrokni. Overlapping clusters for distributed computation. WS- DM '12, pages 273-282, 2012.
5. Reid Andersen and Kevin J. Lang. An algorithm for improving graph partitions. SODA, pages 651-660, 2008.
6. Reid Andersen and Yuval Peres. Finding sparse cuts locally using evolving sets. STOC, 2009.
7. 2) time. SIAM Journal on Computing, 39(5):1748-1771, 2010.
8. Sanjeev Arora and Satyen Kale. A combinatorial, primal-dual approach to semidefinite programs. STOC '07, pages 227-236, 2007.
9. Sanjeev Arora, Satish Rao, and Umesh V. Vazirani. Expander flows, geometric embeddings and graph partitioning. Journal of the ACM, 56(2), 2009.
10. Shuchi Chawla, Robert Krauthgamer, Ravi Kumar, Yuval Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. Computational Complexity, 15(2):94-114, June 2006.
11. E. A. Dinic. Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Math Doklady, 11:1277-1280, 1970.
12. Uriel Feige and Robert Krauthgamer. A polylogarith- mic approximation of the minimum bisection. SIAM J. Comput., 31(4), April 2002.
13. Giorgio Gallo, Michael D. Grigoriadis, and Robert E. Tarjan. A fast parametric maximum flow algorithm and applications. SIAM Journal on Computing, 18(1):30- 55, February 1989.
14. Ullas Gargi, Wenjun Lu, Vahab S. Mirrokni, and Sangho Yoon. Large-scale community detection on youtube for topic discovery and exploration. In Conference on Weblogs and Social Media, 2011.
15. Shayan Oveis Gharan and Luca Trevisan. Approximating the expansion profile and almost optimal local graph clustering. FOCS, pages 187-196, 2012.
16. David F. Gleich and C. Seshadhri. Vertex neighborhoods, low conductance cuts, and good seeds for local community methods. In KDD '2012, 2012.
17. Andrew V. Goldberg and Satish Rao. Beyond the flow decomposition barrier. Journal of the ACM, 45(5) :783- 797, September 1998.
18. Chris Harrelson, Kirsten Hildrum, and Satish Rao. A polynomial-time tree decomposition to minimize congestion. SPAA '03, pages 34-43, 2003.
19. George Karypis and Vipin Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359-392, January 1998.
20. Rohit Khandekar, Satish Rao, and Umesh Vazirani. Graph partitioning using single commodity flows. In STOC '06, 2006.
21. Tsz Chiu Kwok, Lap Chi Lau, Yin Tat Lee, Shayan Oveis Gharan, and Luca Trevisan. Improved cheeger's inequality: Analysis of spectral partitioning algorithms through higher order spectral gap. In STOC '13, January 2013.
22. Kevin Lang and Satish Rao. A flow-based method for improving the expansion or conductance of graph cuts. Integer Programming and Combinatorial Optimization, 3064:325-337, 2004.
23. Frank Thomson Leighton and Satish Rao. Multicom- modity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM, 46(6):787-832, 1999.
24. Michael W. Mahoney, Lorenzo Orecchia, and Nisheeth K. Vishnoi. A local spectral method for graphs: With applications to improving graph partitions and exploring data graphs locally. Journal of Machine Learning Research, 13:2339-2365, 2012.
25. Konstantin Makarychev, Yury Makarychev, and Aravindan Vijayaraghavan. Approximation algorithms for semi-random partitioning problems. In STOC '12, pages 367-384, 2012.
26. Rajeev Motwani and Prabhakar Raghavan. Randomized algorithms. Cambridge University Press, New York, NY, USA, 1995.
27. Lorenzo Orecchia, Sushant Sachdeva, and Nisheeth K. Vishnoi. Approximating the exponential, the lanczos method and an 0(m)-time spectral algorithm for balanced separator. In STOC '12. ACM Press, November 2012.
28. Lorenzo Orecchia, Leonard J. Schulman, Umesh V. Vazirani, and Nisheeth K. Vishnoi. On partitioning graphs via single commodity flows. In STOC 08, New York, New York, USA, 2008.
29. Lorenzo Orecchia and Zeyuan Allen Zhu. Flow-based algorithms for local graph clustering. CoRR, ab- s/1307.2855, 2013.
30. Jonah Sherman. Breaking the multicommodity flow barrier for o(√log n)approximations to sparsest cut. FOCS '09, pages 363-372, 2009.
31. Alistair Sinclair and Mark Jerrum. Approximate counting, uniform generation and rapidly mixing markov chains. Information and Computation, 82(1):93-133, 1989.
32. Daniel D. Sleator and Robert Endre Tarjan. A data structure for dynamic trees. Journal of computer and system sciences, 26(3), 1983.
33. Daniel A. Spielman and Shang-Hua Teng. Nearly- linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. STOC, pages 81-90, 2004.
34. Daniel A. Spielman and Shang-Hua Teng. A local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning. SIAM Journal on Computing, 42(1):1-26, January 2013.
35. Zeyuan Allen Zhu, Silvio Lattanzi, and Vahab Mirrokni. A local algorithm for finding well-connected clusters. In ICML, 2013.