Abstract
This paper provides a study on the rendezvous problem in which two anonymous mobile entities referred to as robots \(r_A\) and \(r_B\) are asked to meet at an arbitrary node of a graph \(G = (V,E)\). As opposed to more standard assumptions robots may not be able to visit the entire graph G. Namely, each robot has its own map which is a connected subgraph of G. Such mobility restrictions may be dictated by the topological properties combined with the intrinsic characteristics of robots preventing them from visiting certain edges in E.
We consider four different variants of the rendezvous problem introduced in [Farrugia et al. SOFSEM’15] which reflect on restricted maneuverability and navigation ability of \(r_A\) and \(r_B\) in G. In the latter, the focus is on models in which robots’ actions are synchronised. The authors prove that one of the maps must be a subgraph of the other. I.e., without this assumption (or some extra knowledge) the rendezvous problem does not have a feasible solution. In this paper, while we keep the containment assumption, we focus on asynchronous robots and the relevant bounds in the four considered variants. We provide some impossibility results and almost tight lower and upper bounds when the solutions are possible.
Work supported in part by the European project “Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies” (GEO-SAFE), contract no. H2020-691161, and by the Italian National Group for Scientific Computation (GNCS-INdAM).
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Cicerone, S., Di Stefano, G., Gąsieniec, L., Navarra, A. (2019). Asynchronous Rendezvous with Different Maps. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_11
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