Abstract
Given a tree T = (V, E) with n vertices and a collection of terminal sets D = {S 1, S 2, …, 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′ ⊆ 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 + 2k) 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.
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Liu, H., Zhang, P. (2012). On the Generalized Multiway Cut in Trees Problem. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_14
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DOI: https://doi.org/10.1007/978-3-642-31770-5_14
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