Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6894567 | European Journal of Operational Research | 2018 | 26 Pages |
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 hâ¯â¤â¯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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Hadrien Cambazard, Nicolas Catusse,