Theoretical Computer Science
On quasi orders of words and the confluence property
Theoretical Computer Science
The structure of information pathways in a social communication network
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
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
Parsimonious flooding in dynamic graphs
Proceedings of the 28th ACM symposium on Principles of distributed computing
Scalable Routing in Cyclic Mobile Networks
IEEE Transactions on Parallel and Distributed Systems
Distributed computation in dynamic networks
Proceedings of the forty-second ACM symposium on Theory of computing
Information Spreading in Stationary Markovian Evolving Graphs
IEEE Transactions on Parallel and Distributed Systems
Characterizing topological assumptions of distributed algorithms in dynamic networks
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
On the power of waiting when exploring public transportation systems
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
IEEE Communications Surveys & Tutorials
Building a reference combinatorial model for MANETs
IEEE Network: The Magazine of Global Internetworking
On the exploration of time-varying networks
Theoretical Computer Science
Time-varying graphs and dynamic networks
International Journal of Parallel, Emergent and Distributed Systems
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Time-varying graphs model in a natural way infrastructure-less highly dynamic systems, such as wireless ad-hoc mobile networks, robotic swarms, vehicular networks, etc. In these systems, a path from a node to another might still exist over time, rendering computing possible, even though at no time the path exists in its entirety. Some of these systems allow waiting (i.e., provide the nodes with store-carry-forward-like mechanisms such as local buffering) while others do not. In this paper, we focus on the structure of the time-varying graphs modelling these highly dynamical environments. We examine the complexity of these graphs, with respect to waiting, in terms of their expressivity; that is in terms of the language generated by the feasible journeys (i.e., the "paths over time"). We prove that the set of languages ${\cal L}_{nowait}$ when no waiting is allowed contains all computable languages. On the other end, using algebraic properties of quasi-orders, we prove that ${\cal L}_{wait}$ is just the family of regular languages, even if the presence of edges is controlled by some arbitrary function of the time. In other words, we prove that, when waiting is allowed, the power of the accepting automaton drops drastically from being as powerful as a Turing machine, to becoming that of a Finite-State machine. This large gap provides a measure of the impact of waiting. We also study bounded waiting; that is when waiting is allowed at a node for at most d time units. We prove that ${\cal L}_{wait[d]} = {\cal L}_{nowait}$; that is, the complexity of the accepting automaton decreases only if waiting is unbounded.