Exploration of Periodically Varying Graphs
Paola Flocchini, Bernard Mans, Nicola Santoro

TL;DR
This paper investigates the exploration problem in periodically varying graphs, establishing necessary conditions, lower bounds, and providing optimal algorithms for different system types, advancing understanding of dynamic network exploration.
Contribution
It introduces tight bounds and necessary conditions for exploration in PV graphs, along with simple, optimal algorithms for anonymous and id-equipped systems.
Findings
Necessary and sufficient conditions for exploration
Lower bounds on exploration time in PV graphs
Constructive algorithms for optimal exploration
Abstract
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. In fact we prove that all necessary conditions are also sufficient and all lower bounds on costs are tight.…
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Taxonomy
TopicsOpportunistic and Delay-Tolerant Networks · Optimization and Search Problems · Human Mobility and Location-Based Analysis
