SIAM Journal on Applied Mathematics
Journal of Computer and System Sciences
Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
Regular Article: The Diameter of Sparse Random Graphs
Advances in Applied Mathematics
Protocols and Impossibility Results for Gossip-Based Communication Mechanisms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Models and Techniques for Communication in Dynamic Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Optimal Controlled Flooding Search in a Large Wireless Network
WIOPT '05 Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Information dissemination in highly dynamic graphs
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in 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
Broadcasting in dynamic radio networks
Journal of Computer and System Sciences
Parsimonious flooding in dynamic graphs
Proceedings of the 28th ACM symposium on Principles of distributed computing
Information spreading in stationary Markovian evolving graphs
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
Information spreading in dynamic graphs
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
On the exploration of time-varying networks
Theoretical Computer Science
An efficient generator for clustered dynamic random networks
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
| Hi-index | 0.01 |
=1We introduce stochastic time-dependency in evolving graphs: starting from an initial graph, at every time step, every edge changes its state (existing or not) according to a two-state Markovian process with probabilities $p$ (edge birth-rate) and $q$ (edge death-rate). If an edge exists at time $t$, then, at time $t+1$, it dies with probability $q$. If instead the edge does not exist at time $t$, then it will come into existence at time $t+1$ with probability $p$. Such an evolving graph model is a wide generalization of time-independent dynamic random graphs [A. E. F. Clementi, A. Monti, F. Pasquale, and R. Silvestri, J. Comput. System Sci., 75 (2009), pp. 213-220] and will be called edge-Markovian evolving graphs. We investigate the speed of information spreading in such evolving graphs. We provide nearly tight bounds (which in fact turn out to be tight for a wide range of probabilities $p$ and $q$) on the completion time of the flooding mechanism aiming to broadcast a piece of information from a source node to all nodes. In particular, we provide i) a tight characterization of the class of edge-Markovian evolving graphs where flooding time is constant and, thus, it does not asymptotically depend on the initial graph; ii) a tight characterization of the class of edge-Markovian evolving graphs where flooding time does not asymptotically depend on the edge death-rate $q$. An interesting consequence of our results is that information spreading can be fast even if the graph, at every time step, is very sparse and disconnected. Furthermore, our bounds imply that the flooding time can be exponentially shorter than the mixing time of the edge-Markovian graph.