On the generalized multiway cut in trees problem

  • Authors:

  • Hong Liu;Peng Zhang

  • Affiliations:

  • School of Computer Science and Technology, Shandong University, Jinan, China 250101;School of Computer Science and Technology, Shandong University, Jinan, China 250101

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

Quantified Score

Hi-index 0.00

Visualization

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