On the generalized multiway cut in trees problem

Hong Liu () and Peng Zhang ()
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Hong Liu: Shandong University
Peng Zhang: Shandong University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 1, No 6, 65-77

Abstract: 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

Keywords: Internal Vertex; Dynamic Programming Approach; Input Tree; Greedy Approach; Problem Kernel (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-012-9565-9

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