Feldmann, A.E. orcid.org/0000-0001-6229-5332, Issac, D. and Rai, A. (2020) Fixed-parameter tractability of the weighted edge clique partition problem. In: Cao, Y. and Pilipczuk, M., (eds.) Leibniz International Proceedings in Informatics, LIPIcs. 15th International Symposium on Parameterized and Exact Computation (IPEC 2020), 14-18 Dec 2020, Virtual conference. Leibniz International Proceedings in Informatics, 180 . Schloss Dagstuhl--Leibniz-Zentrum , Dagstuhl, Germany , 17:1-17:16. ISBN 978-3-95977-172-6
Abstract
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 2O(k2)nO(1) [Issac, 2019]. For WECP we develop a compression (to a slightly more general problem) with 4k vertices, and an algorithm with runtime 2O(k3/2w1/2 log(k/w))nO(1), where w is the maximum edge weight. The latter in particular improves the runtime for ECP to 2O(k3/2 logk)nO(1).
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Edge Clique Partition; fixed-parameter tractability; kernelization |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Jun 2023 11:54 |
Last Modified: | 28 Jun 2023 13:51 |
Status: | Published |
Publisher: | Schloss Dagstuhl--Leibniz-Zentrum |
Series Name: | Leibniz International Proceedings in Informatics |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.IPEC.2020.17 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200947 |