eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
44:1
44:14
10.4230/LIPIcs.ICALP.2018.44
article
Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs
Duan, Ran
1
Gu, Yong
1
Zhang, Le
1
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
We present improved algorithms for solving the All Pairs Non-decreasing Paths (APNP) problem on weighted digraphs. Currently, the best upper bound on APNP is O~(n^{(9+omega)/4})=O(n^{2.844}), obtained by Vassilevska Williams [TALG 2010 and SODA'08], where omega<2.373 is the usual exponent of matrix multiplication. Our first algorithm improves the time bound to O~(n^{2+omega/3})=O(n^{2.791}). The algorithm determines, for every pair of vertices s, t, the minimum last edge weight on a non-decreasing path from s to t, where a non-decreasing path is a path on which the edge weights form a non-decreasing sequence. The algorithm proposed uses the combinatorial properties of non-decreasing paths. Also a slightly improved algorithm with running time O(n^{2.78}) is presented.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.44/LIPIcs.ICALP.2018.44.pdf
Graph algorithms
Matrix multiplication
Non-decreasing paths