Skip to main content

Research Repository

Advanced Search

Temporal network optimization subject to connectivity constraints

Mertzios, G.B.; Michail, O.; Spirakis, P.G.

Temporal network optimization subject to connectivity constraints Thumbnail


Authors

O. Michail

P.G. Spirakis



Abstract

In this work we consider temporal networks, i.e. networks defined by a labeling λ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by λ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.

Citation

Mertzios, G., Michail, O., & Spirakis, P. (2019). Temporal network optimization subject to connectivity constraints. Algorithmica, 81(4), 1416-1449. https://doi.org/10.1007/s00453-018-0478-6

Journal Article Type Article
Acceptance Date Jun 28, 2018
Online Publication Date Jul 5, 2018
Publication Date Apr 30, 2019
Deposit Date Jun 28, 2018
Publicly Available Date Mar 28, 2024
Journal Algorithmica
Print ISSN 0178-4617
Electronic ISSN 1432-0541
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 81
Issue 4
Pages 1416-1449
DOI https://doi.org/10.1007/s00453-018-0478-6

Files


Published Journal Article (Advance online version) (1.2 Mb)
PDF

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Advance online version © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.






You might also like



Downloadable Citations