Geometry, flows, and graph-partitioning algorithms

Communications of the ACM

Volumn 51, Issue 10, 2008, Pages 96-105

  Arora, Sanjeev ^a   Rao, Satish ^b   Vazirani, Umesh ^b  

^a Princeton University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER VISION; EDGE DETECTION; GRAPH THEORY; IMAGE ANALYSIS; IMAGE PROCESSING; IMAGE SEGMENTATION; SET THEORY; STATISTICAL METHODS; TOPOLOGY;

COMPUTATIONAL PROBLEMS; DATA ANALYSIS; DRAW-IN; EUCLIDEAN METRIC; FAST ALGORITHMS; FLOW BASED; GEOMETRIC APPROACHES; GEOMETRIC SPACE; GRAPH PARTITIONING; METRIC SPACES; PARTITIONING ALGORITHMS; SUM OF SQUARES;

COMPUTATIONAL GEOMETRY;

EID: 53349160856     PISSN: 00010782     EISSN: 15577317     Source Type: Journal    
DOI: 10.1145/1400181.1400204     Document Type: Article

References (18)

1. Alan, N. Eigenvalues and expanders, Cambinatarica, 6(2):83-96, 1986.
2. 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. Sac. 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. III (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 sernidefinite programming, J. Assoc. Camput. 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 Camput, 20(1):359-392, 1998,
12. Khandekar, R., Rao, S., and Vazlrani, 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. Lelghton, T. and Rao, S. Multlcommodity max-flow mln-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. Cambinatorica, 15(2):215-245, 1995.
16. Orecchia, L., Schulman, L., Vazlrani, U., and Vlshnoin, 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.