N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate Max-Flow Min-(multi)cut Theorems and Their Applications. SIAM Journal on Computing 25:235-251, 1996. Preliminary version appeared in STOC '93. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Approximation Algorithms for the 0-Extension Problem - Calinescu, Karloff, Rabani (11 citations) (Correct)
....V n T induces a planar graph, is an alternative constant ratio approximation algorithm for some of these computer vision problems. Another problem related to ours is the multicut problem, first considered in the context of approximation algorithms in two papers by Garg, Vazirani, and Yannakakis [7, 8] (and implicitly in Klein, Agarwal, Ravi, and Rao [12] In this problem, we are given a (weighted) graph and k pairs of terminals (nodes in the graph) and the goal is to find a set of edges of minimum weight whose removal disconnects every pair of terminals. This is a different generalization of ....
....every pair of terminals. This is a different generalization of multiway cut (the latter can be viewed as the multicut problem for all Gamma k 2 Delta pairs of terminals) It is incomparable to the 0 extension problem, in the sense that neither problem is a special case of the other. In [8], Garg et al. give an O(log jT j) approximation algorithm for the multicut problem, based on a metric relaxation (assign lengths to edges so that the distance between every specified pair of terminals is at least 1) Their result is tight for the relaxation. The example achieving (asymptotically) ....
N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. SIAM J. Comput. 25:235-251, 1996. Preliminary version appeared in STOC '93.
Approximation Algorithms for the 0-Extension Problem - Calinescu, Karloff, Rabani (2000) (11 citations) (Correct)
....V n T induces a planar graph, is an alternative constant ratio approximation algorithm for some of these computer vision problems. Another problem related to ours is the multicut problem, first considered in the context of approximation algorithms in two papers by Garg, Vazirani, and Yannakakis [7, 8] (and implicitly in Klein, Agarwal, Ravi, and Rao [12] In this problem, we are given a (weighted) graph and k pairs of terminals (nodes in the graph) and the goal is to find a set of edges of minimum weight whose removal disconnects every pair of terminals. This is a different generalization of ....
....disconnects every pair of terminals. This is a different generalization of multiway cut (the latter can be viewed as the multicut problem for all k 2 pairs of terminals) It is incomparable to the 0 extension problem, in the sense that neither problem is a special case of the other. In [8], Garg et al. give an O(log jT j) approximation algorithm for the multicut problem, based on a metric relaxation (assign lengths to edges so that the distance between every specified pair of terminals is at least 1) Their result is tight for the relaxation. The example achieving (asymptotically) ....
N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. SIAM J. Comput. 25:235-251, 1996. Preliminary version appeared in STOC '93.
Multiway Cut - Calinescu, Karloff, Rabani (1998) (Correct)
....easier than its vertex or directed variations. Finally, Hu [18] proposed Minimum Multicut as an integral dual to maximum multicommodity flow. In this problem, we have to disconnect a list of pairs of terminals. Multiway Cut is a special case, in which the list of pairs forms a clique. Garg et al. [14] give a O(log k) approximation algorithm for Minimum Multicut. As noted in [9] a multiway cut algorithm can be used to approximate minimum multicut by the same ratio with running time polynomial in n and 2 k . Therefore, our algorithm gives better approximation guarantees for Minimum Multicut ....
N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate Max-Flow Min-(multi)cut Theorems and Their Applications. SIAM Journal on Computing 25:235-251, 1996. Preliminary version appeared in STOC '93.
An Improved Approximation Algorithm for Multiway Cut - Calinescu, Karloff, Rabani (1998) (16 citations) Self-citation (Cut) (Correct)
....is easier than its node or directed variations. Finally, Hu [18] proposed Minimum Multicut as an integral dual to maximum multicommodity flow. In this problem, we have to disconnect a list of pairs of terminals. Multiway Cut is a special case, in which the list of pairs forms a clique. Garg et al. [14] give a O(log k) approximation algorithm for Minimum Multicut. As noted in [9] a multiway cut algorithm can be used to approximate minimum multicut by the same ratio with running time polynomial in n and 2 k . Therefore, our algorithm gives better approximation guarantees for Minimum Multicut ....
N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate Max-Flow Min-(multi)cut Theorems and Their Applications. SIAM Journal on Computing 25:235-251, 1996. Preliminary version appeared in STOC '93.
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