文章基本信息

标题：Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs
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作者：Karl Bringmann ; Thomas Dueholm Hansen ; Sebastian Krinninger 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：124:1-124:16
DOI：10.4230/LIPIcs.ICALP.2017.124
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with n nodes and m edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time ~O(m^{3/4} n^{3/2}), which gives the first improvement over Megiddo's ~O(n^3) algorithm [JACM'83] for sparse graphs (We use the notation ~O(.) to hide factors that are polylogarithmic in n.) We further demonstrate how to obtain both an algorithm with running time n^3/2^{Omega(sqrt(log n)} on general graphs and an algorithm with running time ~O(n) on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest.
关键词：quantitative verification and synthesis; parametric search; shortest paths; negative cycle detection