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The Complexity of Multiterminal Cuts
 SIAM Journal on Computing
, 1994
"... In the Multiterminal Cut problem we are given an edgeweighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, maxflow problem, and ..."
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In the Multiterminal Cut problem we are given an edgeweighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, maxflow problem, and can be solved in polynomial time. We show that the problem becomes NPhard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NPhard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2  2/k of the optimal cut weight.
Finding kcuts within Twice the Optimal
, 1995
"... Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for find ..."
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Cited by 45 (2 self)
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Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for finding a set of nearoptimal kcuts, one for each value of k between 2 and n. i 1 Introduction The minimum kcut problem is as follows: given an undirected graph G = (V; E) with nonnegative edge weights and a positive integer k, find a set S ` E of minimum weight whose removal leaves k connected components. This problem is of considerable practical significance, especially in the area of VLSI design. Solving this problem exactly is NPhard [GH], but no efficient approximation algorithms were known for it. In this paper we give two simple algorithms for finding kcuts. We prove a performance guarantee of (2 \Gamma 2=k) for each algorithm; however, neither algorithm dominates the other on a...
Finding k cuts within twice the optimal
 SIAM Journal on Computing
, 1995
"... Abstract. Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a k cut having weight within a factor of (2 2/k) of the optimal. One algorithm is particularly efficientit requires a total of only n maximum flow computations for finding a set of near ..."
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Abstract. Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a k cut having weight within a factor of (2 2/k) of the optimal. One algorithm is particularly efficientit requires a total of only n maximum flow computations for finding a set of nearoptimal k cuts, one for each value of k between 2 and n. Key words, graph partitioning, minimum cuts, approximation algorithms AMS subject classifications. 68Q20, 68Q25