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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. 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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    7. 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.
    8. 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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