On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Connectivity and inference problems for temporal networks
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Models and Techniques for Communication in Dynamic Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Labeling Schemes for Flow and Connectivity
SIAM Journal on Computing
Computation in networks of passively mobile finite-state sensors
Distributed Computing - Special issue: PODC 04
Flooding time in edge-Markovian dynamic graphs
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Distributed computation in dynamic networks
Proceedings of the forty-second ACM symposium on Theory of computing
Theoretical Computer Science
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
Time-varying graphs and dynamic networks
International Journal of Parallel, Emergent and Distributed Systems
Causality, influence, and computation in possibly disconnected synchronous dynamic networks
Journal of Parallel and Distributed Computing
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In this work we consider temporal networks, i.e. networks defined by a labelingλ assigning to each edge of an underlying graphG 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.