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Temporal network optimization subject to connectivity constraints.

Mertzios, G.B. and Michail, O. and Spirakis, P.G. (2019) 'Temporal network optimization subject to connectivity constraints.', Algorithmica., 81 (4). pp. 1416-1449.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00453-018-0478-6
Publisher statement:© 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.
Date accepted:28 June 2018
Date deposited:29 June 2018
Date of first online publication:05 July 2018
Date first made open access:No date available

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