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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| Published in: | European journal of operational research Vol. 270; no. 2; pp. 419 - 429 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
16.10.2018
Elsevier |
| Subjects: | |
| ISSN: | 0377-2217, 1872-6860 |
| Online Access: | Get full text |
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| Summary: | •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. |
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| ISSN: | 0377-2217 1872-6860 |
| DOI: | 10.1016/j.ejor.2018.03.042 |