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 -