@MISC{Dumitrescu15constant-factorapproximation, author = {Adrian Dumitrescu and Csaba D. Tóth}, title = {Constant-Factor Approximation for TSP with Disks}, year = {2015} }

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Abstract

We revisit the traveling salesman problem with neighborhoods (TSPN) and present the first constant-ratio approximation for disks in the plane: Given a set of n disks in the plane, a TSP tour whose length is at most O(1) times the optimal with high probability can be computed in time that is polynomial in n. Our result is the first constant-ratio approximation for a class of planar convex bodies of arbitrary size and arbitrary intersections. In order to achieve a O(1)-approximation, we reduce the traveling salesman problem with disks, up to constant factors, to a minimum weight hitting set problem in a geometric hyper-graph. The connection between TSPN and hitting sets in geometric hypergraphs, established here, is likely to have future applications.