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On the generalized multiway cut in trees problem

Author

Listed:
  • Hong Liu

    (Shandong University)

  • Peng Zhang

    (Shandong University)

Abstract

Given a tree $$T = (V, E)$$ with $$n$$ vertices and a collection of terminal sets $$D = \{S_1, S_2, \ldots , S_c\}$$ , where each $$S_i$$ is a subset of $$V$$ and $$c$$ is a constant, the generalized multiway cut in trees problem (GMWC(T)) asks to find a minimum size edge subset $$E^{\prime } \subseteq E$$ such that its removal from the tree separates all terminals in $$S_i$$ from each other for each terminal set $$S_i$$ . The GMWC(T) problem is a natural generalization of the classical multiway cut in trees problem, and has an implicit relation to the Densest $$k$$ -Subgraph problem. In this paper, we show that the GMWC(T) problem is fixed-parameter tractable by giving an $$O(n^2 + 2^k)$$ time algorithm, where $$k$$ is the size of an optimal solution, and the GMWC(T) problem is polynomial time solvable when the problem is restricted in paths.We also discuss some heuristics for the GMWC(T) problem

Suggested Citation

  • Hong Liu & Peng Zhang, 2014. "On the generalized multiway cut in trees problem," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 65-77, January.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:1:d:10.1007_s10878-012-9565-9
    DOI: 10.1007/s10878-012-9565-9
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    References listed on IDEAS

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    1. David R. Karger & Philip Klein & Cliff Stein & Mikkel Thorup & Neal E. Young, 2004. "Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 436-461, August.
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    Cited by:

    1. Xiaofei Liu & Weidong Li, 2022. "Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1964-1976, October.
    2. Xiaofei Liu & Weidong Li, 0. "Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.

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