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

•A fixed-parameter algorithm for the rectilinear travelling salesman problem.•A fixed-parameter algorithm for the rectilinear Steiner tree problem.•A refined complexity analysis.•Experimental results showing the scalability of this approach. Given a set P of n points with their pairwise distances, t...

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Veröffentlicht in:European journal of operational research Jg. 270; H. 2; S. 419 - 429
Hauptverfasser: Cambazard, Hadrien, Catusse, Nicolas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.10.2018
Elsevier
Schlagworte:
Computer Science
Fixed-parameter algorithm
Operations Research
Rectilinear Steiner tree problem
Rectilinear traveling salesman problem
Traveling salesman
Traveling salesman
Rectilinear Steiner tree problem
Fixed-parameter algorithm
Rectilinear traveling salesman problem
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•A fixed-parameter algorithm for the rectilinear travelling salesman problem.•A fixed-parameter algorithm for the rectilinear Steiner tree problem.•A refined complexity analysis.•Experimental results showing the scalability of this approach. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2018.03.042