An Approximation Algorithm for the Three Depots Hamiltonian Path Problem

  • Aristotelis GiannakosEmail author
  • M’hand Hifi
  • Rezika Kheffache
  • Rachid Ouafi
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 31)


In this paper, we propose an approximation algorithm for solving the three depots Hamiltonian path problem (3DHPP). The problem studied can be viewed as a variant of the well-known Hamiltonian path problem with multiple depots (cf., Demange [Mathématiques et Informatique, Gazette, 102 (2004)] and Malik et al. [Oper. Res. Lett. 35, 747–753 (2007)]). For the 3DHPP, we show the existence of a \(\frac{3} {2}\)-approximation algorithm for a broad family of metric cases which also guarantees a ratio r < 2 in the general metric case. The proposed algorithm is mainly based on extending the construction scheme already used by Rathinam et al. [Oper. Res. Lett. 38, 63–68 (2010)]. The aforementioned result is established for a variant of the three-depot problem, that is, when costs are symmetric and satisfy the triangle inequality.

Key words

Approximation algorithms Hamiltonian path problem Traveling salesman problem 


  1. 1.
    Bresovec, C., Cornuejols, G., Glover, F.: A matroid algorithm and its application to the efficient solution of two optimization problems on graphs. Math. Program. 42, 471–487 (1998)CrossRefGoogle Scholar
  2. 2.
    Cerdeira, J.O.: Matroids and a forest cover problem. Math. Program. 66, 403–405 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Demange, M.: Algorithme d’approximation: un petit tour en compagnie d’un voyageur de commerce. Lagazette des Mathématiques. 102, 51–90 (2004)Google Scholar
  4. 4.
    Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Natl. Bur. Stand. 69B, 125–130 (1965)MathSciNetGoogle Scholar
  5. 5.
    Lawler, E.L.: Combinatorial Optimisation: Networks and Matroids. Dover Publication, New York (2001)zbMATHGoogle Scholar
  6. 6.
    Malik, W., Rathinam, S., Darbha, S.: An approximation algorithm for a symmetric generalized multiple depot, multiple traveling salesman problem. Oper. Res. Lett. 35, 747–753 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Rathinam, S., Sengupta, R.: \(\frac{3} {2}\)-approximation algorithm for two variants of 2-depot Hamiltonian path problem. Oper. Res. Lett. 38, 63–68 (2010).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Aristotelis Giannakos
    • 1
    Email author
  • M’hand Hifi
    • 1
  • Rezika Kheffache
    • 2
  • Rachid Ouafi
    • 3
  1. 1.Picardie UniversityAmiens Cedex 1France
  2. 2.Faculty of Science Tizi OuzonMouloud Mammeri UniversityTizi-OuzouAlgeria
  3. 3.University of TechnologyBab EzzouarAlgeria

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