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Geometry, flows, and graph-partitioning algorithms

Published: 01 October 2008 Publication History
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References

[1]
Alon, N. Eigenvalues and expanders. Combinatorica, 6(2):83--96, 1986.
[2]
Arora, S., Hazan, E., and Kale, S. O(\sqrt {\log n)}) approximation to sparsest cut in Õ(n 2) time. In FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04), pages 238--247, Washington, DC, USA, 2004. IEEE Computer Society.
[3]
Arora, S., Hazan, E., and Kale, S. Multiplicative weights method: a meta-algorithm and its applications---a survey, 2005.
[4]
Arora, S. and Kale, S. A combinatorial, primal-dual approach to semidefinite programs. In STOC '07: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, pages 227--236, New York, NY, USA, 2007. ACM.
[5]
Arora, S., Lee, J. R., and Naor, A. Euclidean distortion and the sparsest cut. J. Amer Math, Soc., 21(1):1--21 2008 (Electronic).
[6]
Arora, S., Rao, S., and Vazirani, U. Expander flows, geometric embeddings and graph partitioning. In STOC '04: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, pages 222--231, New York, NY, USA, 2004. ACM.
[7]
Chawla, S., Gupta, A., and Raecke, H. Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut. In SODA '05: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms. pages 102--111, Philadelphia, PA, USA, 2005. Society for Industrial and Applied Mathematics.
[8]
Cheeger, J. A lower bound for the smallest eigenvalue of the Laplacian. In Problem in Analysis, pages 195--199, 1970.
[9]
Goemans, M. X. Semidefinite programming and combinatorial optimization. In Proceedings of the International Congress of Mathematicians, Vol. Ill (Berlin, 1998), pages 657--666,1998 (electronic).
[10]
Goemans, M. X. and Williamson, D. P. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach., 42(6):1115--1145, 1995.
[11]
Karypis, G. and Kumar, V. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Scientific Comput., 20(l):359--392, 1998.
[12]
Khandekar, R., Rao, S., and Vazirani, U. Graph partitioning using single commodity flows. In STOC '06: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, pages 385--390, New York, NY, USA, 2006. ACM Press.
[13]
Lee, J. R. On distance scales, embeddings, and efficient relaxations of the cut cone. In SODA '05: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 92--101, Philadelphia, PA, USA, 2005. Society for Industrial and Applied Mathematics.
[14]
Leighton, T. and Rao, S. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. J. ACM (JACM), 46(6):787--832, 1999.
[15]
Linial, N., London, E., and Rabinovich, Y. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215--245, 1995.
[16]
Orecchia, L., Schulman, L. Vazirani U., and Vishnoin, N. On partitioning graphs via single commodity flows. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17--20, 2008. pages 461--470, 2008.
[17]
Shmoys, D. S. Cut problems and their application to divide and conquer. In D. S. Hochbaum, ed., Approximation Algorithms for NP-Hard Problems. PWS Publishing, 1995.
[18]
Sinclair, A. and Jerrum, M. Approximate counting, uniform generation and rapidly mixing Markov chains (extended abstract). In Graph-Theoretic Concepts in Computer Science (Staffelstein, 1987), volume 314 of Lecture Notes in Comput. Sci., pages 134--148, Berlin, 1988. Springer.

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        cover image Communications of the ACM
        Communications of the ACM  Volume 51, Issue 10
        October 2008
        130 pages
        ISSN:0001-0782
        EISSN:1557-7317
        DOI:10.1145/1400181
        Issue’s Table of Contents
        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 ACM 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]

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        Published: 01 October 2008
        Published in CACM Volume 51, Issue 10

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