2026-08-15T09:05:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8631 2024-03-06T10:42:11Z ddc:004 open_access

Evacuating an Equilateral Triangle in the Face-to-Face Model Chuangpishit, Huda Mehrabi, Saeed Narayanan, Lata Opatrny, Jaroslav Distributed algorithms Robots evacuation Face-to-face communication Equilateral triangle 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Huda Chuangpishit and Saeed Mehrabi and Lata Narayanan and Jaroslav Opatrny 2018 Is Part Of LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.OPODIS.2017.11 urn:nbn:de:0030-drops-86310 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.11 eng https://creativecommons.org/licenses/by/3.0/legalcode