Abstract
Two hikers and a bike are initially placed at the origin of an infinite line. When walking, the hikers can keep a constant speed of 1, but when riding the bike they can reach a constant speed \(v>1\) (same for both hikers). The hikers are modelled as autonomous mobile robots with communication capabilities (either in the wireless or face-to-face model) while the bike is not autonomous in that it cannot move on its own but instead it must be picked up by a hiker. An exit is placed on the line at distance d from the origin; the distance and direction of the exit from the origin is unknown to the hikers. The hikers may either walk or ride the bike however only one hiker may ride the bike at a time. The goal of the hikers is to evacuate from the exit in the minimum time possible as measured by the time it takes the last hiker to exit.
We develop algorithms for this “bike assisted” evacuation of the two hikers from an unknown exit on a line and analyze their evacuation time. In the wireless model we present three algorithms: in the first the robots move in opposite direction with max speed, in the second with a specially selected “optimal” speed, and in the third the hiker imitates the biker. We also give three algorithms in the Face-to-Face model: in the first algorithm the hiker pursues the biker, in the second the hiker and the biker use zig-zag algorithms with specially chosen expansion factors, and the third algorithm establishes a sequence a specially constructed meeting points near the exit. In either case, the optimality of these algorithms depends on \(v >1\). We also discuss lower bounds.
E. Kranakis—Research supported in part by NSERC Discovery grant.
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Notes
- 1.
The present study is revised and updated from the first author’s MCS Thesis [15].
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Jawhar, K., Kranakis, E. (2021). Bike Assisted Evacuation on a Line. In: Bureš, T., et al. SOFSEM 2021: Theory and Practice of Computer Science. SOFSEM 2021. Lecture Notes in Computer Science(), vol 12607. Springer, Cham. https://doi.org/10.1007/978-3-030-67731-2_8
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