Communication and location discovery in geometric ring networks

Gasieniec, Leszek ORCID: 0000-0003-1809-9814, Jurdzinski, Tomasz, Martin, Russell ORCID: 0000-0002-7043-503X and Stachowiak, Grzegorz (2019) Communication and location discovery in geometric ring networks. INFORMATION AND COMPUTATION, 266. pp. 19-48.

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Abstract

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronized rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that n mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The location discovery task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem. Assuming that agents are anonymous (there are no IDs distinguishing them), our solution applied to randomly chosen IDs from appropriately chosen range gives an (almost) optimal algorithm, improving upon the complexity of previous randomized results.

Item Type:	Article
Uncontrolled Keywords:	Mobile robots, Distributed algorithms, Location discovery, Boundary patrolling, Combinatorial structures
Depositing User:	Symplectic Admin
Date Deposited:	20 Dec 2018 11:35
Last Modified:	19 Jan 2023 01:08
DOI:	10.1016/j.ic.2018.12.001
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3030285