Approximating minimum label s-t cut via linear programming

  • Authors:

  • Linqing Tang;Peng Zhang

  • Affiliations:

  • State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China;School of Computer Science and Technology, Shandong University, Jinan, China

  • Venue:
  • LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
  • Year:
  • 2012

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Abstract

We consider the Minimum Label s-t Cut problem. Given an undirected graph G=(V,E) with a label set L, in which each edge has a label from L, and a source s∈V together with a sink t∈V, the goal of the Minimum Label s-t Cut problem is to pick a subset of labels of minimized cardinality, such that the removal of all edges with these labels from G disconnects s and t. We present a min { O((m/OPT)1/2), O(n2/3/OPT1/3) }-approximation algorithm for the Minimum Label s-t Cut problem using linear programming technique, where n=|V|, m=|E|, and OPT is the optimal value of the input instance. This result improves the previously best known approximation ratio O(m1/2) for this problem (Zhang et al., JOCO 21(2), 192---208 (2011)), and gives the first approximation ratio for this problem in terms of n. Moreover, we show that our linear program relaxation for the Minimum Label s-t Cut problem, even in a stronger form, has integrality gap Ω((m/OPT)1/2−ε).