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Faster Exploration of Degree-Bounded Temporal Graphs

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conference contribution
posted on 30.07.2018, 11:12 by Thomas Erlebach, Jakob T. Spooner
A temporal graph can be viewed as a sequence of static graphs indexed by discrete time steps. The vertex set of each graph in the sequence remains the same; however, the edge sets are allowed to differ. A natural problem on temporal graphs is the Temporal Exploration problem (TEXP): given, as input, a temporal graph G of order n, we are tasked with computing an exploration schedule (i.e., a temporal walk that visits all vertices in G), such that the time step at which the walk arrives at the last unvisited vertex is minimised (we refer to this time step as the arrival time). It can be easily shown that general temporal graphs admit exploration schedules with arrival time no greater than O(n^2). Moreover, it has been shown previously that there exists an infinite family of temporal graphs for which any exploration schedule has arrival time Ω(n^2), making these bounds tight for general TEXP instances. We consider restricted instances of TEXP, in which the temporal graph given as input is, in every time step, of maximum degree d; we show an O(n^2/log n) bound on the arrival time when d is constant, and an O(d log d · n^2 / log n) bound when d is given as some function of n.

History

Citation

Proceedings of the 43rd International Symposium on Mathematical Foundations of Computer Science, 2018, pp. 36:1-36:13 (13)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Informatics

Source

43rd International Symposium on Mathematical Foundations of Computer Science. MFCS 2018, Liverpool

Version

VoR (Version of Record)

Published in

Proceedings of the 43rd International Symposium on Mathematical Foundations of Computer Science

Publisher

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

eissn

1868-8969

Acceptance date

13/06/2018

Copyright date

2018

Available date

07/09/2018

Publisher version

http://drops.dagstuhl.de/opus/volltexte/2018/9618

Temporal coverage: start date

27/08/2018

Temporal coverage: end date

31/08/2018

Language

en