Single Approximation for Biobjective Max TSP

  • Cristina Bazgan
  • Laurent Gourvès
  • Jérôme Monnot
  • Fanny Pascual
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7164)


We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analysed in three cases. When both (resp. at least one) objective function(s) fulfill(s) the triangle inequality, the approximation ratio is \(\frac{5}{12}-\varepsilon\approx 0.41\) (resp. \(\frac{3}{8}-\varepsilon\)). When the triangle inequality is not assumed on any objective function, the algorithm is \(\frac{1+2\sqrt{2}}{14} -\varepsilon\approx 0.27\)-approximate.


Polynomial Time Triangle Inequality Travel Salesman Problem Minimum Weight Hamiltonian Cycle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 2
    • 3
  • Laurent Gourvès
    • 1
    • 2
  • Jérôme Monnot
    • 1
    • 2
  • Fanny Pascual
    • 4
  1. 1.LAMSADEUniversité Paris-DauphineParis Cedex 16France
  2. 2.CNRSUMR 7243France
  3. 3.Institut Universitaire de FranceFrance
  4. 4.LIP6Université Pierre et Marie CurieParisFrance

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