eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
17:1
17:16
10.4230/LIPIcs.IPEC.2020.17
article
Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem
Feldmann, Andreas Emil
1
https://orcid.org/0000-0001-6229-5332
Issac, Davis
2
https://orcid.org/0000-0001-5559-7471
Rai, Ashutosh
1
https://orcid.org/0000-0003-2429-750X
Department of Applied Mathematics, Charles University, Prague, Czech Republic
Hasso Plattner Institute, Potsdam, Germany
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).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.17/LIPIcs.IPEC.2020.17.pdf
Edge Clique Partition
fixed-parameter tractability
kernelization