Fixed-Parameter Algorithms for Rectilinear Steiner tree and Rectilinear
Traveling Salesman Problem in the plane
release_2kl3awikgva5zabkfgiujjnvom
by
Hadrien Cambazard, Nicolas Catusse
2016
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 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 ≤ 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.
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