Edge exploration of temporal graphs

Bumpus, B. M. and Meeks, K. (2023) Edge exploration of temporal graphs. Algorithmica, 85(3), pp. 688-716. (doi: 10.1007/s00453-022-01018-7)

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We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast to the static case, it is NP-hard to determine whether a given temporal graph is temporally Eulerian even if strong restrictions are placed on the structure of the underlying graph and each edge is active at only three times. However, we do obtain an FPT-algorithm with respect to a new parameter called interval-membership-width which restricts the times assigned to different edges; we believe that this parameter will be of independent interest for other temporal graph problems. Our techniques also allow us to resolve two open questions of Akrida, Mertzios and Spirakis [CIAC 2019] concerning a related problem of exploring temporal stars.

Item Type:Articles
Additional Information:The first author was supported by an EPSRC doctoral training account and also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 803421, ReduceSearch). The second author was supported by a Royal Society of Edinburgh Personal Research Fellowship, funded by the Scottish Government, and EPSRC grant EP/T004878/1.
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty and Bumpus, Benjamin
Authors: Bumpus, B. M., and Meeks, K.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Algorithmica
ISSN (Online):1432-0541
Published Online:22 August 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Algorithmica 85(3) 688-716
Publisher Policy:Reproduced under a Creative Commons License

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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
172865EPSRC DTP 16/17 and 17/18Mary Beth KneafseyEngineering and Physical Sciences Research Council (EPSRC)EP/N509668/1Research and Innovation Services