Note: Parameterized complexity of k-Chinese Postman Problem

  • Authors:

  • Gregory Gutin;Gabriele Muciaccia;Anders Yeo

  • Affiliations:

  • Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682, Singapore and Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

We consider the following problem called the k-Chinese Postman Problem (k-CPP): given a connected edge-weighted graph G and integers p and k, decide whether there are at least k closed walks such that every edge of G is contained in at least one of them and the total weight of the edges in the walks is at most p? The problem k-CPP is NP-complete, and van Bevern et al. [4] and Sorge [14] asked whether the k-CPP is fixed-parameter tractable when parameterized by k. We prove that the k-CPP is indeed fixed-parameter tractable. In fact, we prove a stronger result: the problem admits a kernel with O(k^2logk) vertices. We prove that the directed version of k-CPP is NP-complete and ask whether the directed version is fixed-parameter tractable when parameterized by k.