License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2022.20
URN: urn:nbn:de:0030-drops-173764
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17376/
Komusiewicz, Christian ;
Morawietz, Nils
Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial
Abstract
A k-swap W for a vertex cover S of a graph G is a vertex set of size at most k such that S' = (S ⧵ W) ∪ (W ⧵ S), the symmetric difference of S and W, is a vertex cover of G. If |S'| < |S|, then W is improving. In LS-Vertex Cover, one is given a vertex cover S of a graph G and wants to know if there is an improving k-swap for S in G. In applications of LS-Vertex Cover, k is a very small parameter that can be set by a user to determine the trade-off between running time and solution quality. Consequently, k can be considered to be a constant. Motivated by this and the fact that LS-Vertex Cover is W[1]-hard with respect to k, we aim for algorithms with running time ?^f(k) ⋅ n^?(1) where ? is a structural graph parameter upper-bounded by n. We say that such a running time grows mildly with respect to ? and strongly with respect to k. We obtain algorithms with such a running time for ? being the h-index of G, the treewidth of G, or the modular-width of G. In addition, we consider a novel parameter, the maximum degree over all quotient graphs in a modular decomposition of G. Moreover, we adapt these algorithms to the more general problem where each vertex is assigned a weight and where we want to find a d-improving k-swap, that is, a k-swap which decreases the weight of the vertex cover by at least d.
BibTeX - Entry
@InProceedings{komusiewicz_et_al:LIPIcs.IPEC.2022.20,
author = {Komusiewicz, Christian and Morawietz, Nils},
title = {{Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial}},
booktitle = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
pages = {20:1--20:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-260-0},
ISSN = {1868-8969},
year = {2022},
volume = {249},
editor = {Dell, Holger and Nederlof, Jesper},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17376},
URN = {urn:nbn:de:0030-drops-173764},
doi = {10.4230/LIPIcs.IPEC.2022.20},
annote = {Keywords: Local Search, Structural parameterization, Fixed-parameter tractability}
}
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Keywords: |
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Local Search, Structural parameterization, Fixed-parameter tractability |
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Collection: |
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17th International Symposium on Parameterized and Exact Computation (IPEC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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14.12.2022 |
