Fixed-Parameter Algorithms for Rectilinear Steiner tree and Rectilinear Traveling Salesman Problem in the plane [article]

Hadrien Cambazard, Nicolas Catusse
2017 arXiv   pre-print
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 l_1 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(nh7^h) where h ≤
more » ... 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(nh5^h) time complexity. Both bounds improve over the best time bounds known for these problems.
arXiv:1512.06649v3 fatcat:a3hk3u3rmbhnjm4usmrevsonhy