Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems

  • Authors:

  • Markus Bläser;L. Shankar Ram;Maxim Sviridenko

  • Affiliations:

  • Institut für Theoretische Informatik, ETH Zürich, Zürich, Switzerland;Institut für Theoretische Informatik, ETH Zürich, Zürich, Switzerland;IBM T.J. Watson Research Center

  • Venue:
  • WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
  • Year:
  • 2005

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Abstract

We consider an APX-hard variant (Δ-Max-ATSP) and an APX-hard relaxation (Max-3-DCC) of the classical traveling salesman problem. Δ-Max-ATSP is the following problem: Given an edge-weighted complete loopless directed graph G such that the edge weights fulfill the triangle inequality, find a maximum weight Hamiltonian tour of G. We present a $\frac{31}{40}$-approximation algorithm for Δ-Max-ATSP with polynomial running time. Max-3-DCC is the following problem: Given an edge-weighted complete loopless directed graph, compute a spanning collection of node-disjoint cycles, each of length at least three, whose weight is maximum among all such collections. We present a $\frac{3}{4}$-approximation algorithm for this problem with polynomial running time. In both cases, we improve on the previous best approximation performances. The results are obtained via a new decomposition technique for the fractional solution of an LP formulation of Max-3-DCC.