2026-07-22T18:58:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6420 2024-03-06T10:38:12Z ddc:004 open_access

New Parameterized Algorithms for APSP in Directed Graphs Porat, Ely Shahbazian, Eduard Tov, Roei Graphs distances APSP fast matrix multiplication All Pairs Shortest Path (APSP) is a classic problem in graph theory. While for general weighted graphs there is no algorithm that computes APSP in O(n^{3-epsilon}) time (epsilon > 0), by using fast matrix multiplication algorithms, we can compute APSP in O(n^{omega}*log(n)) time (omega < 2.373) for undirected unweighted graphs, and in O(n^{2.5302}) time for directed unweighted graphs. In the current state of matters, there is a substantial gap between the upper bounds of the problem for undirected and directed graphs, and for a long time, it is remained an important open question whether it is possible to close this gap. In this paper we introduce a new parameter that measures the symmetry of directed graphs (i.e. their closeness to undirected graphs), and obtain a new parameterized APSP algorithm for directed unweighted graphs, that generalizes Seidel's O(n^{omega}*log(n)) time algorithm for undirected unweighted graphs. Given a directed unweighted graph G, unless it is highly asymmetric, our algorithms can compute APSP in o(n^{2.5}) time for G, providing for such graphs a faster APSP algorithm than the state-of-the-art algorithms for the problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ely Porat and Eduard Shahbazian and Roei Tov 2016 Is Part Of LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2016.72 urn:nbn:de:0030-drops-64207 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.72 eng https://creativecommons.org/licenses/by/3.0/legalcode