Approximate max-flow min-(multi)cut theorems and their applications

SIAM Journal on Computing

Volumn 25, Issue 2, 1996, Pages 235-251

  Garg, Naveen ^a   Vazirani, Vijay V ^a   Yannakakis, Mihalis ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

Approximation algorithm; Minimum multicut; Multicommodity flow

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; GRAPH THEORY; RELAXATION PROCESSES; THEOREM PROVING;

APPROXIMATE MAX FLOW MINCUT THEOREMS; APPROXIMATION ALGORITHM; MINIMUM MULTICUT; MULTICOMMODITY FLOW;

ALGORITHMS;

EID: 0030127682     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539793243016     Document Type: Article

References (19)

1. S. ARORA, C. LUND, R. MOTWANI, M. SUNDAN, AND M. SZEGEDY, Proof verification and hardness of approximation problems, in Proc. 32nd IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1992, pp. 14-23.
2. B. AWERBUCH, Complexity of network synchronization, J. Assoc. Comput. Mach., 32 (1985), pp. 804-823.
3. W. H. CUNNINGHAM, The optimal multiterminal cut problem, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 5 (1991), pp. 105-120.
4. E. DAHLHAUS, D. S. JOHNSON, C. H. PAPADIMITRIOU, P. D. SEYMOUR, AND M. YANNAKAKIS, The complexity of multiway cuts, in Proc. 24th ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1992, pp. 241-251.
5. P. ELIAS, A. FEINSTEIN, AND C. F. SHANNON, A note on the maximum flow through a network, IRE Trans. Inform. Theory IT, 2 (1956), pp. 117-119.
6. L. R. FORT, JR. AND D. R. FULKERSON, Maximal flow through a network, Canad. J. Math., 8 (1956).
7. N. GARG AND V. V. VAZIRANI, A characterization of the vertices and edges of the s-t cut polyhedron, with algorithmic applications, in Proc. Integer Programming and Combinatorial Optimization, 1993.
8. N. GARG, V. V. VAZIRANI, AND M. YANNAKAKIS, Primal-dual approximation algorithms for integral flow and multicut in trees, with applications to matching and set cover, in Proc. 20th International Collection on Automata, Languages, and Programming, Springer-Verlag, Berlin, New York, Heidelberg, 1992, pp. 64-75.
9. T. C. HU, Multicommodity network flows, Oper. Res., 11 (1963), pp. 344-360.
10. P. KLEIN, A. AGRAWAL, R. RAVI, AND S. RAO, Approximation through multicommodity flow, in Proc. 31st Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1990, pp. 726-737.
11. P. KLEIN, S. PLOTKIN, AND S. RAO, Excluded minors, network decomposition, and multi-commodity flow, in Proc. 25th ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1992, pp. 682-690.
12. P. KLEIN, C. STEIN, AND E. TARDOS, Leighton-Rao might be practical: faster opproximation algorithms for concurrent flow with uniform capacities, in Proc. 22nd ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1990, pp. 310-321.
13. F. T. LEIGHTON AND S. RAO, An approximate max-flow min-cut theorem for uniform multicommodity flow problems with application to approximation algorithms, in Proc. 29th IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1988, pp. 422-431.
14. C. H. PAPADIMITRIOU AND M. YANNAKAKIS, Optimization, approximation and complexity classes, J. Comput. System Sci., 43 (1991), pp. 425-440.
15. S. PLOTKIN AND E. TARDOS, Improved bounds on the max-flow min-cut ratio for multicommodity flows, in Proc. 25th ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1992, pp. 691-697.
16. r,r-free graphs, Inform. Process. Lett., 47 (1993), pp. 77-80.
17. S. TRAGOUDAS, Improved approximation for the minimum-cut ratio and the flux, Math. Systems Theory, to appear.
18. M. YANNAKAKIS, Edge-deletion problems, SIAM J. Comput., 10 (1981), pp. 297-309.
19. M. YANNAKAKIS, P. C. KANELLAKIS, S. C. COSMADAKIS, AND C. H. PAPADIMITRIOU, Cutting and partitioning a graph after a fixed pattern, in Proc. 10th International Collection on Automata, Languages, and Programming, Springer-Verlag, Berlin, New York, Heidelberg, 1983, pp. 712-722.