Professor Thomas Erlebach thomas.erlebach@durham.ac.uk
Professor Computer Science
Exploration of k-Edge-Deficient Temporal Graphs
Erlebach, Thomas; Spooner, Jakob T.
Authors
Jakob T. Spooner
Abstract
A temporal graph with lifetime L is a sequence of L graphs G1, . . . , GL, called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always-connected if each layer is a connected graph, and it is k-edge-decient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always- connected, k-edge-decient temporal graphs with sucient lifetime can always be explored in O(kn log n) time steps. We also construct always-connected, k-edge- decient temporal graphs for which any exploration requires (n log k) time steps. For always-connected, 1-edge-decient temporal graphs, we show that O(n) time steps suce for temporal exploration.
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 28, 2022 |
Online Publication Date | Aug 27, 2022 |
Publication Date | 2022-08 |
Deposit Date | Apr 10, 2022 |
Publicly Available Date | Aug 30, 2022 |
Journal | Acta Informatica |
Print ISSN | 0001-5903 |
Electronic ISSN | 1432-0525 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 59 |
Issue | 4 |
Pages | 387-407 |
DOI | https://doi.org/10.1007/s00236-022-00421-5 |
Public URL | https://durham-repository.worktribe.com/output/1210332 |
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