文章基本信息

标题：Approximating the Regular Graphic TSP in Near Linear Time
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作者：Ashish Chiplunkar ; Sundar Vishwanathan
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：45
页码：125-135
DOI：10.4230/LIPIcs.FSTTCS.2015.125
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We present a randomized approximation algorithm for computing traveling salesperson tours in undirected regular graphs. Given an n-vertex, k-regular graph, the algorithm computes a tour of length at most (1+frac 4+ln 4+varepsilon ln k-O(1)n, with high probability, in O(nk log k) time. This improves upon the result by Vishnoi ([Vishnoi12],FOCS 2012) for the same problem, in terms of both approximation factor, and running time. Furthermore, our result is incomparable with the recent result by Feige, Ravi, and Singh ([FeigeRS14], IPCO 2014), since our algorithm runs in linear time, for any fixed k. The key ingredient of our algorithm is a technique that uses edge-coloring algorithms to sample a cycle cover with O(n/log k) cycles, with high probability, in near linear time. Additionally, we also give a deterministic frac{3}{2}+O(frac{1}sqrt{k}) factor approximation algorithm for the TSP on n-vertex, k-regular graphs running in time O(nk).
关键词：traveling salesperson problem; approximation; linear time