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An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem


The parameterized node multiway cut problem is for a given graph to find a separator of size bounded by k whose removal separates a collection of terminal sets in the graph. In this paper, we develop an O(k4k n 3) time algorithm for this problem, significantly improving the previous algorithm of time \(O(4^{k^{3}}n^{5})\) for the problem. Our result gives the first polynomial time algorithm for the minimum node multiway cut problem when the separator size is bounded by O(log n).

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Author information

Correspondence to Songjian Lu.

Additional information

A preliminary version of this paper was presented at The 10th Workshop on Algorithms and Data Structures (WADS 2007).

This work was supported in part by the National Science Foundation under the Grants CCR-0311590 and CCF-0430683.

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Chen, J., Liu, Y. & Lu, S. An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem. Algorithmica 55, 1–13 (2009). https://doi.org/10.1007/s00453-007-9130-6

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  • Multiway cut problem
  • Parameterized algorithm
  • Fixed-parameter tractability
  • Minimum cut
  • Network flow