文章基本信息
- 标题：Euclidean TSP in Narrow Strips
- 本地全文：下载
- 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,δ] depends on the strip width δ. 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 log²n) time using an existing algorithm) is guaranteed to be a shortest tour overall when δ ⩽ 2â^S2, a bound which is best possible. - We present an algorithm that is fixed-parameter tractable with respect to δ. More precisely, our algorithm has running time 2^{O(â^Sδ)} n² for sparse point sets, where each 1Ã-δ 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,δ], it has an expected running time of 2^{O(â^Sδ)} n² + O(n³).
- 关键词：Computational geometry; Euclidean TSP; bitonic TSP; fixed-parameter tractable algorithms
