2026-07-23T15:50:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11899 2024-03-06T10:48:58Z ddc:004 open_access

Efficient Parameterized Algorithms for Computing All-Pairs Shortest Paths Kratsch, Stefan Nelles, Florian All-pairs shortest Paths efficient parameterized Algorithms parameterized Complexity Clique-width Modular-width Computing all-pairs shortest paths is a fundamental and much-studied problem with many applications. Unfortunately, despite intense study, there are still no significantly faster algorithms for it than the ?(n³) time algorithm due to Floyd and Warshall (1962). Somewhat faster algorithms exist for the vertex-weighted version if fast matrix multiplication may be used. Yuster (SODA 2009) gave an algorithm running in time ?(n^2.842), but no combinatorial, truly subcubic algorithm is known. Motivated by the recent framework of efficient parameterized algorithms (or "FPT in P"), we investigate the influence of the graph parameters clique-width (cw) and modular-width (mw) on the running times of algorithms for solving ALL-PAIRS SHORTEST PATHS. We obtain efficient (and combinatorial) parameterized algorithms on non-negative vertex-weighted graphs of times ?(cw²n²), resp. ?(mw²n + n²). If fast matrix multiplication is allowed then the latter can be improved to ?(mw^{1.842} n + n²) using the algorithm of Yuster as a black box. The algorithm relative to modular-width is adaptive, meaning that the running time matches the best unparameterized algorithm for parameter value mw equal to n, and they outperform them already for mw ∈ ?(n^{1 - ε}) for any ε > 0. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Stefan Kratsch and Florian Nelles 2020 Is Part Of LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2020.38 urn:nbn:de:0030-drops-118992 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.38 eng https://creativecommons.org/licenses/by/3.0/legalcode