A New Temporal Interpretation of Cluster Editing

Bocci, C., Capresi, C., Meeks, K. and Sylvester, J. (2022) A New Temporal Interpretation of Cluster Editing. In: 33rd International Workshop in Combinatorial Algorithms (IWOCA 2022), Trier, Germany, 07-09 Jun 2022, ISBN 9783031066771 (doi: 10.1007/978-3-031-06678-8_16)

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Abstract

The NP-complete graph problem CLUSTER EDITING seeks to transform a static graph into disjoint union of cliques by making the fewest possible edits to the edge set. We introduce a natural interpretation of this problem in the setting of temporal graphs, whose edge-sets are subject to discrete changes over time, which we call EDITING TO TEMPORAL CLIQUES. This problem is NP-complete even when restricted to temporal graphs whose underlying graph is a path, but we obtain two polynomial-time algorithms for special cases with further restrictions. In the static setting, it is well-known that a graph is a disjoint union of cliques if and only if it contains no induced copy of P3; we demonstrate that there can be no universal characterisation of cluster temporal graphs in terms of subsets of at most four vertices. However, subject to a minor additional restriction, we obtain a characterisation involving forbidden configurations on five vertices. This characterisation gives rise to an FPT algorithm parameterised simultaneously by the permitted number of modifications and the lifetime of the temporal graph, which uses a simple search-tree strategy.

Item Type:Conference Proceedings
Additional Information:Meeks and Sylvester gratefully acknowledge funding from the Engineering and Physical Sciences Research Council (ESPRC) grant number EP/T004878/1 for this work, while Meeks was also supported by a Royal Society of Edinburgh Personal Research Fellowship (funded by the Scottish Government).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty and Capresi, Chiara and Sylvester, Dr John
Authors: Bocci, C., Capresi, C., Meeks, K., and Sylvester, J.
College/School:College of Science and Engineering
College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783031066771
Copyright Holders:Copyright © 2022 Springer Nature Switzerland AG
First Published:First published in Lecture Notes in Computer Science, vol 13270
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
305944Multilayer Algorithmics to Leverage Graph StructureKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/T004878/1M&S - Statistics