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Fixed-parameter algorithms for rectilinear Steiner tree and rectilinear traveling salesman problem in the plane

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  • Cambazard, Hadrien
  • Catusse, Nicolas

Abstract

Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance considered between two points is the l1 distance. In this paper, a fixed-parameter algorithm for the Rectilinear TSP is presented and relies on techniques for solving TSP on bounded-treewidth graphs. It proves that the problem can be solved in O(nh7h) where h ≤ n denotes the number of horizontal lines containing the points of P. The same technique can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of P providing a O(nh5h) time complexity. Both bounds improve over the best time bounds known for these problems.

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  • Cambazard, Hadrien & Catusse, Nicolas, 2018. "Fixed-parameter algorithms for rectilinear Steiner tree and rectilinear traveling salesman problem in the plane," European Journal of Operational Research, Elsevier, vol. 270(2), pages 419-429.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:419-429
    DOI: 10.1016/j.ejor.2018.03.042
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    References listed on IDEAS

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    Cited by:

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    2. Briant, Olivier & Cambazard, Hadrien & Cattaruzza, Diego & Catusse, Nicolas & Ladier, Anne-Laure & Ogier, Maxime, 2020. "An efficient and general approach for the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 285(2), pages 497-512.
    3. Mustapha Haouassi & Yannick Kergosien & Jorge E. Mendoza & Louis-Martin Rousseau, 2022. "The integrated orderline batching, batch scheduling, and picker routing problem with multiple pickers: the benefits of splitting customer orders," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 614-645, September.
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    5. Diefenbach, Heiko & Grosse, Eric H. & Glock, Christoph H., 2024. "Human-and-cost-centric storage assignment optimization in picker-to-parts warehouses," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1049-1068.
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    7. Neves-Moreira, Fábio & Amorim, Pedro, 2024. "Learning efficient in-store picking strategies to reduce customer encounters in omnichannel retail," International Journal of Production Economics, Elsevier, vol. 267(C).
    8. Bock, Stefan, 2024. "Vehicle routing for connected service areas - a versatile approach covering single, hierarchical, and bi-criteria objectives," European Journal of Operational Research, Elsevier, vol. 313(3), pages 905-925.
    9. Dmitry Kruchinin & Vladimir Kruchinin & Yuriy Shablya, 2021. "Method for Obtaining Coefficients of Powers of Bivariate Generating Functions," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    10. Rajabighamchi, Farzaneh & van Hoesel, Stan & Defryn, Christof, 2023. "The order picking problem under a scattered storage policy," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. AERTS, Babiche & CORNELISSENS, Trijntje & SÖRENSEN, Kenneth, 2020. "Solving the joint order batching and picker routing problem, as a clustered vehicle routing problem," Working Papers 2020003, University of Antwerp, Faculty of Business and Economics.
    12. Rajabighamchi, Farzaneh & van Hoesel, Stan & Defryn, Christof, 2023. "Graph reduction for the planar Travelling Salesman Problem," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).

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