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Evacuating an Equilateral Triangle in the Face-to-Face Model

Authors Huda Chuangpishit, Saeed Mehrabi, Lata Narayanan, Jaroslav Opatrny

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Huda Chuangpishit
Saeed Mehrabi
Lata Narayanan
Jaroslav Opatrny

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Huda Chuangpishit, Saeed Mehrabi, Lata Narayanan, and Jaroslav Opatrny. Evacuating an Equilateral Triangle in the Face-to-Face Model. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.OPODIS.2017.11

Abstract

Consider k robots initially located at the centroid of an equilateral triangle T of sides of length one. The goal of the robots is to evacuate T through an exit at an unknown location on the boundary of T. Each robot can move anywhere in T independently of other robots with maximum speed one. The objective is to minimize the evacuation time, which is defined as the time required for all k robots to reach the exit. We consider the face-to-face communication model for the robots: a robot can communicate with another robot only when they meet in T.
In this paper, we give upper and lower bounds for the face-to-face evacuation time by k robots. We show that for any k, any algorithm for evacuating k >= 1 robots from T requires at least sqrt(3) time. This bound is asymptotically optimal, as we show that a straightforward strategy of evacuation by k robots gives an upper bound of sqrt(3) + 3/k. For k = 3, 4, 5, 6, we
show significant improvements on the obvious upper bound by giving algorithms with evacuation times of 2.0887, 1.9816, 1.876, and 1.827, respectively. For k = 2 robots, we give a lower bound of 1 + 2/sqrt(3) ~= 2.154, and an algorithm with upper bound of 2.3367 on the evacuation time.

Subject Classification

Keywords
  • Distributed algorithms
  • Robots evacuation
  • Face-to-face communication
  • Equilateral triangle

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