IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v266y2018i2p436-457.html
   My bibliography  Save this article

Improved integrality gap upper bounds for traveling salesperson problems with distances one and two

Author

Listed:
  • Mnich, Matthias
  • Mömke, Tobias

Abstract

We prove new integrality gap upper bounds for the traveling salesperson problem with distances one and two ((1,2)-TSP). We obtain these bounds by investigating the structure of the support graph of optimal solutions to the subtour elimination linear programming relaxation, with one additional cutting plane inequality.

Suggested Citation

  • Mnich, Matthias & Mömke, Tobias, 2018. "Improved integrality gap upper bounds for traveling salesperson problems with distances one and two," European Journal of Operational Research, Elsevier, vol. 266(2), pages 436-457.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:436-457
    DOI: 10.1016/j.ejor.2017.09.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717308792
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.09.036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, vol. 12(3), pages 253-313, November.
    2. Christos H. Papadimitriou & Mihalis Yannakakis, 1993. "The Traveling Salesman Problem with Distances One and Two," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 1-11, February.
    3. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    4. Frans Schalekamp & David P. Williamson & Anke van Zuylen, 2014. "2-Matchings, the Traveling Salesman Problem, and the Subtour LP: A Proof of the Boyd-Carr Conjecture," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 403-417, May.
    5. WOLSEY, Laurence A., 1980. "Heuristic analysis, linear programming and branch and bound," LIDAM Reprints CORE 407, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    2. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    3. Sivakumar, Rathinam & Sengupta, Raja, 2007. "5/3-Approximation Algorithm for a Multiple Depot, Terminal Hamiltonian Path Problem," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3dw086dn, Institute of Transportation Studies, UC Berkeley.
    4. Rathinam, Sivakumar & Sengupta, Raja, 2007. "3/2-Approximation Algorithm for a Generalized, Multiple Depot, Hamiltonina Path Problem," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt06p2815q, Institute of Transportation Studies, UC Berkeley.
    5. Moses Charikar & Michel X. Goemans & Howard Karloff, 2006. "On the Integrality Ratio for the Asymmetric Traveling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 245-252, May.
    6. Gábor Braun & Samuel Fiorini & Sebastian Pokutta & David Steurer, 2015. "Approximation Limits of Linear Programs (Beyond Hierarchies)," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 756-772, March.
    7. de Klerk, E. & Pasechnik, D.V. & Sotirov, R., 2007. "On Semidefinite Programming Relaxations of the Travelling Salesman Problem (Replaced by DP 2008-96)," Discussion Paper 2007-101, Tilburg University, Center for Economic Research.
    8. Frans Schalekamp & David P. Williamson & Anke van Zuylen, 2014. "2-Matchings, the Traveling Salesman Problem, and the Subtour LP: A Proof of the Boyd-Carr Conjecture," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 403-417, May.
    9. de Klerk, E. & Pasechnik, D.V. & Sotirov, R., 2008. "On Semidefinite Programming Relaxations of the Traveling Salesman Problem (revision of DP 2007-101)," Discussion Paper 2008-96, Tilburg University, Center for Economic Research.
    10. Miroslav Chlebík & Janka Chlebíková, 2022. "Weighted amplifiers and inapproximability results for Travelling Salesman problem," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1368-1390, July.
    11. Vivek Bagaria & Jian Ding & David Tse & Yihong Wu & Jiaming Xu, 2020. "Hidden Hamiltonian Cycle Recovery via Linear Programming," Operations Research, INFORMS, vol. 68(1), pages 53-70, January.
    12. Valenzuela, Christine L. & Jones, Antonia J., 1997. "Estimating the Held-Karp lower bound for the geometric TSP," European Journal of Operational Research, Elsevier, vol. 102(1), pages 157-175, October.
    13. U. Seppaelae, 1997. "An Evolutionary Model for Spatial Location of Economic Facilities," Working Papers ir97003, International Institute for Applied Systems Analysis.
    14. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.
    15. Rostami, Borzou & Malucelli, Federico & Belotti, Pietro & Gualandi, Stefano, 2016. "Lower bounding procedure for the asymmetric quadratic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 584-592.
    16. Deeparnab Chakrabarty & Chaitanya Swamy, 2016. "Facility Location with Client Latencies: LP-Based Techniques for Minimum-Latency Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 865-883, August.
    17. Harkness, Joseph & ReVelle, Charles, 2003. "Facility location with increasing production costs," European Journal of Operational Research, Elsevier, vol. 145(1), pages 1-13, February.
    18. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    19. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    20. Federico Della Croce, 2016. "MP or not MP: that is the question," Journal of Scheduling, Springer, vol. 19(1), pages 33-42, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:436-457. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.