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A 3/2-Approximation Algorithm for Multiple Depot Multiple Traveling Salesman Problem

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Algorithm Theory - SWAT 2010 (SWAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6139))

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Abstract

As an important extension of the classical traveling salesman problem (TSP), the multiple depot multiple traveling salesman problem (MDMTSP) is to minimize the total length of a collection of tours for multiple vehicles to serve all the customers, where each vehicle must start or stay at its distinct depot. Due to the gap between the existing best approximation ratios for the TSP and for the MDMTSP in literature, which are 3/2 and 2, respectively, it is an open question whether or not a 3/2-approximation algorithm exists for the MDMTSP. We have partially addressed this question by developing a 3/2-approximation algorithm, which runs in polynomial time when the number of depots is a constant.

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References

  1. Arkin, E.M., Hassin, R., Levin, A.: Approximations for minimum and min-max vehicle routing problems. Journal of Algorithms 59(1), 1–18 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem, Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University (1976)

    Google Scholar 

  3. Eiselt, H.A., Gendreau, M., Laporte, G.: Arc routing problems, part i: The chinese postman problem. Operations Research 43(2), 231–242 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eiselt, H.A., Gendreau, M., Laporte, G.: Arc routing problems, part ii: The rural postman problem. Operations Research 43(3), 399–414 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  6. Giosa, I.D., Tansini, I.L., Viera, I.O.: New assignment algorithms for the multi-depot vehicle routing problem. Journal of the Operational Research Society 53(9), 977–984 (2002)

    Article  MATH  Google Scholar 

  7. Lim, A., Wang, F.: Multi-depot vehicle routing problem: a one-stage approach. IEEE Transactions on Automation Science and Engineering 2(4), 397–402 (2005)

    Article  Google Scholar 

  8. Malik, W., Rathinam, S., Darbha, S.: An approximation algorithm for a symmetric generalized multiple depot, multiple travelling salesman problem. Operations Research Letters 35(6), 747–753 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Papadimitriou, C.H., Steiglitz, K.: Approximation algorithms for the traveling salesman problem. In: Combinatorial Optimization: Algorithms and Complexity, pp. 410–419. Courier Dover Publications (1998)

    Google Scholar 

  10. Rathinam, S., Sengupta, R.: 3/2-Approximation Algorithm for a Generalized, Multiple Depot, Hamiltonina Path Problem. Technical report, University of California, Berkeley (2007)

    Google Scholar 

  11. Rathinam, S., Sengupta, R.: 5/3-approximation algorithm for a multiple depot, terminal hamiltonian path problem. Technical report, University of California, Berkeley (2007)

    Google Scholar 

  12. Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multi-vehicle systems with non holonomic constraints. IEEE Transactions on Automation Sciences and Engineering 4(1), 98–104 (2006)

    Article  Google Scholar 

  13. Rathinama, S., Senguptab, R.: 3/2-approximation algorithm for two variants of a 2-depot hamiltonian path problem. Operations Research Letters 38(1), 63–68 (2010)

    Article  MathSciNet  Google Scholar 

  14. Renaud, J., Laporte, G., Boctor, F.F.: A tabu search heuristic for the multi-depot vehicle routing problem. Computers and Operations Research 23(3), 229–235 (1996)

    Article  MATH  Google Scholar 

  15. Rosenkrantz, D.J., Stearns, R.E., Lewis, P.M.: An analysis of several heuristics for the traveling salesman problem. SIAM Journal on Computing 6(3), 563–581 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wolsey, L.A., Nemhauser, G.L.: Integer and Combinatorial Optimization, ch. section III.3, p. 664. Wiley-Interscience, Hoboken (1988)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Business, The Hong Kong Polytechnic University,  

    Zhou Xu

  2. Lee Kong Chian School of Business, Singapore Management University,  

    Brian Rodrigues

Authors
  1. Zhou Xu
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  2. Brian Rodrigues
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Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Haim Kaplan

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Xu, Z., Rodrigues, B. (2010). A 3/2-Approximation Algorithm for Multiple Depot Multiple Traveling Salesman Problem . In: Kaplan, H. (eds) Algorithm Theory - SWAT 2010. SWAT 2010. Lecture Notes in Computer Science, vol 6139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13731-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-13731-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13730-3

  • Online ISBN: 978-3-642-13731-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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