Temporal Network Optimization Subject to Connectivity Constraints

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

doi:10.1007/978-3-642-39212-2_57

Temporal Network Optimization Subject to Connectivity Constraints

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

Authors

Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor

O. Michail

I. Chatzigiannakis

P.G. Spirakis

Contributors

Fedor V. Fomin
Editor

Rūsiņš Freivalds
Editor

Marta Kwiatkowska
Editor

David Peleg
Editor

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., Chatzigiannakis, I., & Spirakis, P. (2013). Temporal Network Optimization Subject to Connectivity Constraints. In F. V. Fomin, R. Freivalds, M. Kwiatkowska, & D. Peleg (Eds.), Automata, languages, and programming : 40th international colloquium, ICALP 2013, Riga, Latvia, July 8 - 12, 2013, proceedings, part II (657-668). Springer Verlag. https://doi.org/10.1007/978-3-642-39212-2_57

Publication Date	2013
Deposit Date	Sep 5, 2014
Publicly Available Date	Jun 22, 2015
Publisher	Springer Verlag
Pages	657-668
Series Title	Lecture notes in computer science
Book Title	Automata, languages, and programming : 40th international colloquium, ICALP 2013, Riga, Latvia, July 8 - 12, 2013, proceedings, part II.
ISBN	9783642392115
DOI	https://doi.org/10.1007/978-3-642-39212-2_57