Tight Bounds for Deterministic High-Dimensional Grid Exploration

Sebastian Brandt, Julian Portmann, Jara Uitto

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

We study the problem of exploring an oriented grid with autonomous agents governed by finite automata. In the case of a 2-dimensional grid, the question how many agents are required to explore the grid, or equivalently, find a hidden treasure in the grid, is fully understood in both the synchronous and the semi-synchronous setting. For higher dimensions, Dobrev, Narayanan, Opatrny, and Pankratov [ICALP'19] showed very recently that, surprisingly, a (small) constant number of agents suffices to find the treasure, independent of the number of dimensions, thereby disproving a conjecture by Cohen, Emek, Louidor, and Uitto [SODA'17]. Dobrev et al. left as an open question whether their bounds on the number of agents can be improved. We answer this question in the affirmative for deterministic finite automata: we show that 3 synchronous and 4 semi-synchronous agents suffice to explore an n-dimensional grid for any constant n. The bounds are optimal and notably, the matching lower bounds already hold in the 2-dimensional case. Our techniques can also be used to make progress on other open questions asked by Dobrev et al.: we prove that 4 synchronous and 5 semi-synchronous agents suffice for polynomial-time exploration, and we show that, under a natural assumption, 3 synchronous and 4 semi-synchronous agents suffice to explore unoriented grids of arbitrary dimension (which, again, is tight).
Original languageEnglish
Title of host publication34th International Symposium on Distributed Computing (DISC 2020)
Chapter13
Pages1-16
ISBN (Electronic)978-3-95977-168-9
DOIs
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventInternational Symposium on Distributed Computing - Virtual, Online, Germany
Duration: 12 Oct 202016 Oct 2020
Conference number: 32
http://www.disc-conference.org/wp/disc2020/

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Volume179
ISSN (Electronic)1868-8969

Conference

ConferenceInternational Symposium on Distributed Computing
Abbreviated titleDISC
CountryGermany
CityVirtual, Online
Period12/10/202016/10/2020
Internet address

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