TY - JOUR

T1 - Complexity of multiterminal cuts

AU - Dahlhaus, E.

AU - Johnson, D. S.

AU - Papadimitriou, C. H.

AU - Seymour, P. D.

AU - Yannakakis, M.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1994

Y1 - 1994

N2 - In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is 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, max-flow problem, and can be solved in polynomial time. It is shown that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. A simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 - 2/k of the optimal cut weight is also described.

AB - In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is 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, max-flow problem, and can be solved in polynomial time. It is shown that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. A simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 - 2/k of the optimal cut weight is also described.

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U2 - 10.1137/S0097539792225297

DO - 10.1137/S0097539792225297

M3 - Article

AN - SCOPUS:0028484228

VL - 23

SP - 864

EP - 894

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 4

ER -