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A Polynomial Algorithm for the k-Cut Problem for Fixed k

Olivier Goldschmidt and Dorit S. Hochbaum
Mathematics of Operations Research
Vol. 19, No. 1 (Feb., 1994), pp. 24-37
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690374
Page Count: 14
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A Polynomial Algorithm for the k-Cut Problem for Fixed k
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Abstract

The k-cut problem is to find a partition of an edge weighted graph into k nonempty components, such that the total edge weight between components is minimum. This problem is NP-complete for an arbitrary k and its version involving fixing a vertex in each component is NP-hard even for k = 3. We present a polynomial algorithm for k fixed, that runs in $O(n^{k^{2}/2-3k/2+4}T(n,m))$ steps, where T(n, m) is the running time required to find the minimum (s, t)-cut on a graph with n vertices and m edges.

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