文章基本信息

标题：Euclidean TSP in Narrow Strips
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作者：Henk Alkema ; Mark de Berg ; S{'a}ndor Kisfaludi-Bak 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：164
页码：4:1-4:16
DOI：10.4230/LIPIcs.SoCG.2020.4
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We investigate how the complexity of {Euclidean TSP} for point sets P inside the strip (-â^Z,+â^Z)Ã-[0,Î´] depends on the strip width Î´. We obtain two main results. - For the case where the points have distinct integer x-coordinates, we prove that a shortest bitonic tour (which can be computed in O(n logÂ²n) time using an existing algorithm) is guaranteed to be a shortest tour overall when Î´ â©½ 2â^S2, a bound which is best possible. - We present an algorithm that is fixed-parameter tractable with respect to Î´. More precisely, our algorithm has running time 2^{O(â^SÎ´)} nÂ² for sparse point sets, where each 1Ã-Î´ rectangle inside the strip contains O(1) points. For random point sets, where the points are chosen uniformly at random from the rectangle [0,n]Ã- [0,Î´], it has an expected running time of 2^{O(â^SÎ´)} nÂ² + O(nÂ³).
关键词：Computational geometry; Euclidean TSP; bitonic TSP; fixed-parameter tractable algorithms