An Improved Approximation Algorithm for TSP with Distances One and Two

  • M. Bläser
  • L. Shankar Ram
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3623)


The minimum traveling salesman problem with distances one and two is the following problem: Given a complete undirected graph G=(V,E) with a cost function w: E→ {1, 2}, find a Hamiltonian tour of minimum cost. In this paper, we provide an approximation algorithm for this problem achieving a performance guarantee of \(\frac{315}{271}\). This algorithm can be further improved obtaining a performance guarantee of \(\frac{65}{56}\). This is better than the one achieved by Papadimitriou and Yannakakis [8], with a ratio \(\frac{7}{6}\), more than a decade ago. We enhance their algorithm by an involved procedure and find an improved lower bound for the cost of an optimal Hamiltonian tour.


Approximation Algorithm Travel Salesman Problem Travel Salesman Problem Performance Guarantee Span Subgraph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. Bläser
    • 1
  • L. Shankar Ram
    • 1
  1. 1.Institut für Theoretische InformatikETH ZürichZürichSwitzerland

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