2026-08-08T00:46:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13320 2024-03-06T10:51:41Z ddc:004 open_access

Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem Feldmann, Andreas Emil Issac, Davis Rai, Ashutosh Edge Clique Partition fixed-parameter tractability kernelization We develop an FPT algorithm and a compression for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the aim is to find k cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques. It was shown that ECP admits a kernel with k² vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of 2^𝒪(k²)n^O(1) [Issac, 2019]. For WECP we develop a compression (to a slightly more general problem) with 4^k vertices, and an algorithm with runtime 2^𝒪(k^(3/2)w^(1/2)log(k/w))n^O(1), where w is the maximum edge weight. The latter in particular improves the runtime for ECP to 2^𝒪(k^(3/2)log k)n^O(1). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andreas Emil Feldmann and Davis Issac and Ashutosh Rai 2020 Is Part Of LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2020.17 urn:nbn:de:0030-drops-133206 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.17 eng https://creativecommons.org/licenses/by/3.0/legalcode