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Article

Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Department of Computer Science, Kent State University, Kent, OH 44240, USA
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A preliminary version of this article has been published in SSS’17 conference.
Academic Editor: Giovanni Viglietta
Information 2021, 12(11), 448; https://doi.org/10.3390/info12110448
Received: 30 August 2021 / Revised: 18 October 2021 / Accepted: 24 October 2021 / Published: 27 October 2021
(This article belongs to the Special Issue Distributed Systems and Mobile Computing)
We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles following the well-celebrated classic oblivious robots model. We study the fundamental problem of gathering N autonomous robots on a plane, which requires all robots to meet at a single point (or to position within a small area) that is not known beforehand. We consider limited visibility under which robots are only able to see other robots up to a constant Euclidean distance and focus on the time complexity of gathering by robots under limited visibility. There exists an O(DG) time algorithm for this problem in the fully synchronous setting, assuming that the robots agree on one coordinate axis (say north), where DG is the diameter of the visibility graph of the initial configuration. In this article, we provide the first O(DE) time algorithm for this problem in the asynchronous setting under the same assumption of robots’ agreement with one coordinate axis, where DE is the Euclidean distance between farthest-pair of robots in the initial configuration. The runtime of our algorithm is a significant improvement since for any initial configuration of N1 robots, DEDG, and there exist initial configurations for which DG can be quadratic on DE, i.e., DG=Θ(DE2). Moreover, our algorithm is asymptotically time-optimal since the trivial time lower bound for this problem is Ω(DE). View Full-Text
Keywords: distributed algorithms; mobile robots; classic oblivious robot model; gathering; time complexity; visibility; connectivity distributed algorithms; mobile robots; classic oblivious robot model; gathering; time complexity; visibility; connectivity
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MDPI and ACS Style

Poudel, P.; Sharma, G. Time-Optimal Gathering under Limited Visibility with One-Axis Agreement. Information 2021, 12, 448. https://doi.org/10.3390/info12110448

AMA Style

Poudel P, Sharma G. Time-Optimal Gathering under Limited Visibility with One-Axis Agreement. Information. 2021; 12(11):448. https://doi.org/10.3390/info12110448

Chicago/Turabian Style

Poudel, Pavan, and Gokarna Sharma. 2021. "Time-Optimal Gathering under Limited Visibility with One-Axis Agreement" Information 12, no. 11: 448. https://doi.org/10.3390/info12110448

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