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# Approximation Results for Kinetic Variants of TSP

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 Publication Article, peer reviewed scientific Title Approximation Results for Kinetic Variants of TSP Author ; Date 2002 English abstract We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem where we consider instances where points move with fixed constant velocity in a fixed direction. We prove the following results: 1. If the points all move with the same velocity and in the same direction, then there is a PTAS for the Kinetic TSP. 2. The Kinetic TSP cannot be approximated better than by a factor of two by a polynomial time algorithm unless P=NP, even if there are only two moving points in the instance. \item The Kinetic TSP cannot be approximated better than by a factor of $2^{\Omega(\sqrt{n})}$ by a polynomial time algorithm unless P=NP, where $n$ is the size of the input instance, even if the maximum velocity is bounded. DOI https://doi.org/10.1007/s00454-001-0081-4 (link to publisher's fulltext.) Publisher Springer Verlag Host/Issue Discrete and Computational Geometry;4 Volume 27 ISSN 0179-5376 Pages 635-651 Language eng (iso) Subject SciencesResearch Subject Categories::MATHEMATICS::Applied mathematics::Theoretical computer scienceResearch Subject Categories::TECHNOLOGY::Information technology::Computer science::Computer science Handle http://hdl.handle.net/2043/11302 Permalink to this page
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