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On Temporal Graph Exploration

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conference contribution
posted on 07.05.2015, 09:24 by Thomas Erlebach, Michael Hoffmann, F. Kammer
A temporal graph is a graph in which the edge set can change from step to step. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk that starts at a given start node, visits all nodes of the graph, and has the smallest arrival time. We consider only temporal graphs that are connected at each step. For such temporal graphs with $n$ nodes, we show that it is $\NP$-hard to approximate TEXP with ratio $O(n^{1-\epsilon})$ for any $\epsilon>0$. We also provide an explicit construction of temporal graphs that require $\Theta(n^2)$ steps to be explored. We then consider TEXP under the assumption that the underlying graph (i.e. the graph that contains all edges that are present in the temporal graph in at least one step) belongs to a specific class of graphs. Among other results, we show that temporal graphs can be explored in $O(n^{1.5}k^2\log n)$ steps if the underlying graph has treewidth $k$ and in $O(n\log^3 n)$ steps if the underlying graph is a $2\times n$ grid. Finally, we show that sparse temporal graphs with regularly present edges can always be explored in $O(n)$ steps.

History

Citation

Proceedings of the 42nd International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science Volume 9134, 2015, pp. 444-455 (12)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Source

ICALP, Kyoto

Version

AM (Accepted Manuscript)

Published in

Proceedings of the 42nd International Colloquium on Automata

Publisher

Springer Berlin Heidelberg

issn

0302-9743

isbn

978-3-662-47671-0;978-3-662-47672-7

Copyright date

1007

Available date

20/06/2016

Publisher version

http://link.springer.com/chapter/10.1007/978-3-662-47672-7_36

Editors

Speckmann, B.;Kobayashi, N.;Halldorsson, M. M.

Temporal coverage: start date

06/07/2015

Temporal coverage: end date

10/07/2015

Language

en