文章基本信息

标题：Faster Algorithms for All Pairs Non-Decreasing Paths Problem
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作者：Ran Duan ; Ce Jin ; Hongxun Wu 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：132
页码：1-13
DOI：10.4230/LIPIcs.ICALP.2019.48
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time O~(n^{{3 + omega}/{2}}) = O~(n^{2.686}). Here n is the number of vertices, and omega < 2.373 is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for (max, min)-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for (max, min)-matrix product. The previous best upper bound for APNP on weighted digraphs was O~(n^{1/2(3 + {3 - omega}/{omega + 1} + omega)}) = O~(n^{2.78}) [Duan, Gu, Zhang 2018]. We also show an O~(n^2) time algorithm for APNP in undirected simple graphs which also reaches optimal within logarithmic factors.
关键词：graph optimization; matrix multiplication; non-decreasing paths