On the Generalized Multiway Cut in Trees Problem

  • Hong Liu
  • Peng Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)


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 + 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.


Search Tree Internal Vertex Dynamic Programming Approach Input Tree Greedy Approach 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hong Liu
    • 1
  • Peng Zhang
    • 1
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanChina

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