Abstract
Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the environment needed to be revisited with the same minimal frequency.
In this paper we study efficient patrolling protocols for points located on a path, where each point may have a different constraint on frequency of visits. The problem of visiting such divergent points was recently posed by Gąsieniec et al. in [14], where the authors study protocols using a single robot patrolling a set of n points located in nodes of a complete graph and in Euclidean spaces.
The focus in this paper is on patrolling with two robots. We adopt a scenario in which all points to be patrolled are located on a line. We provide several approximation algorithms concluding with the best currently known \(\sqrt{3}\)-approximation.
J. Czyzowicz, K. Georgiou and E. Kranakis—Research supported in part by NSERC.
L. Gąsieniec—Research supported by Networks Sciences and Technologies (NeST).
T. Jurdziński—Research supported by the Polish National Science Centre grant DEC-2012/06/M/ST6/00459.
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Chuangpishit, H., Czyzowicz, J., Gąsieniec, L., Georgiou, K., Jurdziński, T., Kranakis, E. (2018). Patrolling a Path Connecting a Set of Points with Unbalanced Frequencies of Visits. In: Tjoa, A., Bellatreche, L., Biffl, S., van Leeuwen, J., Wiedermann, J. (eds) SOFSEM 2018: Theory and Practice of Computer Science. SOFSEM 2018. Lecture Notes in Computer Science(), vol 10706. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-73117-9_26
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