Constrained minimum vertex cover in bipartite graphs: complexity and parameterized algorithms

  • Authors:

  • Jianer Chen;Iyad A. Kanj

  • Affiliations:

  • Department of Computer Science, Texas A&M University, College Station, TX;School of CTI, DePaul University, 243 S. Wabash Avenue, Chicago, IL

  • Venue:
  • Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
  • Year:
  • 2003

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Abstract

Motivated by the research in reconfigurable memory array structures, this paper studies the complexity and algorithms for the constrained minimum vertex cover problem on bipartite graphs (NIN-CVCB) defined as follows: given a bipartite graph G = (V, E) with vertex bipartition V = U ∪ L and two integers ku and kl, decide whether there is a minimum vertex cover in G with at most ku vertices in U and at most kl vertices in L. It is proved in this paper that the MIN-CVCB problem is NP-complete. This answers a question posed by Hasan and Liu. A parameterized algorithm is developed for the problem, in which classical results in matching theory and recently developed techniques in parameterized computation theory are nicely combined and extended. The algorithm runs in time O(1.26ku + kl + (ku + kl) |G|) and significantly improves previous algorithms for the problem.