How fast can we reach a target vertex in stochastic temporal graphs?

Akrida, Eleni C.; Mertzios, George B.; Nikoletseas, Sotiris; Raptopoulos, Christoforos; Spirakis, Paul G.; Zmaraev, Viktor

Abstract

Temporal graphs abstractly model real-life inherently dynamic networks. Given a graph G, a temporal graph with G as the underlying graph is a sequence of subgraphs (snapshots) of G, where . In this paper we study stochastic temporal graphs, i.e. stochastic processes whose random variables are the snapshots of a temporal graph on G. A natural feature observed in various real-life scenarios is a memory effect in the appearance probabilities of particular edges; i.e. the probability an edge appears at time step t depends on its appearance (or absence) at the previous k steps. We study the hierarchy of models of memory-k, , in an edge-centric network evolution setting: every edge of G has its own independent probability distribution for its appearance over time. We thoroughly investigate the complexity of two naturally related, but fundamentally different, temporal path problems, called Minimum Arrival and Best Policy.

Citation

Akrida, E. C., Mertzios, G. B., Nikoletseas, S., Raptopoulos, C., Spirakis, P. G., & Zmaraev, V. (2020). How fast can we reach a target vertex in stochastic temporal graphs?. Journal of Computer and System Sciences, 114, 65-83. https://doi.org/10.1016/j.jcss.2020.05.005

• Journal Article Type: Article
• Acceptance Date: May 4, 2020
• Online Publication Date: May 28, 2020
• Publication Date: Dec 1, 2020
• Deposit Date: May 8, 2020
• Publicly Available Date: May 28, 2021
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 114
• Pages: 65-83
• DOI: https://doi.org/10.1016/j.jcss.2020.05.005