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Exploration of k-Edge-Deficient Temporal Graphs

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conference contribution
posted on 02.09.2021, 10:47 by Thomas Erlebach, Jakob T Spooner
An always-connected temporal graph G=⟨G1,...,GL⟩ with underlying graph G=(V,E) is a sequence of graphs Gt⊆G such that V(Gt)=V and Gt is connected for all t. This paper considers the property of k-edge-deficiency for temporal graphs; such graphs satisfy Gt=(V,E−Xt) for all t, where Xt⊆E and |Xt|≤k . We study the Temporal Exploration problem (compute a temporal walk that visits all vertices v∈V at least once and finishes as early as possible) restricted to always-connected, k-edge-deficient temporal graphs and give constructive proofs that show that k-edge-deficient and 1-edge-deficient temporal graphs can be explored in O(knlogn) and O(n) timesteps, respectively. We also give a lower-bound construction of an infinite family of always-connected k-edge-deficient temporal graphs for which any exploration schedule requires at least Ω(nlogk) timesteps.

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Citation

Erlebach T., Spooner J.T. (2021) Exploration of k-Edge-Deficient Temporal Graphs. In: Lubiw A., Salavatipour M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science, vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_27

Author affiliation

School of Informatics

Source

17th International Symposium on Algorithms and Data Structures (WADS 2021)

Version

AM (Accepted Manuscript)

Published in

Lecture Notes in Computer Science

Volume

12808

Pagination

371 - 384

Publisher

Springer Verlag

issn

0302-9743

eissn

1611-3349

isbn

9783030835071

Copyright date

2021

Available date

02/09/2021

Spatial coverage

Halifax, Canada (ONLINE)

Temporal coverage: start date

09/08/2021

Temporal coverage: end date

11/08/2021

Language

en

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