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2016 | OriginalPaper | Chapter

Asynchronous Embedded Pattern Formation Without Orientation

Authors : Serafino Cicerone, Gabriele Di Stefano, Alfredo Navarra

Published in: Distributed Computing

Publisher: Springer Berlin Heidelberg

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Abstract

We consider the Embedded Pattern Formation (epf) problem introduced in [Fujinaga et al., SIAM J. on Comput., 44(3), 2015]. Given a set F of distinct points in the Euclidean plane (called here fixed-points) and a set R of robots such that \(|R|=|F|\), the problem asks for a distributed algorithm that moves robots so as to occupy all points in F. Initially, each robot occupies a distinct position.

Robots operate in standard Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of the robots’ positions and the fixed-points (Look) according to its own coordinate system, decides whether to move (Compute), and in the positive case it moves (Move). Cycles are performed asynchronously for each robot. Robots are oblivious, anonymous and execute the same algorithm.

In the mentioned paper, the problem has been investigated by assuming chirality, that is robots share a common left-right orientation. The obtained solution has been used as a sub-procedure to solve the Pattern Formation problem, without fixed-points but still with chirality.

Here we investigate the other branch, that is, we are interested in solving epf without chirality. We fully characterize when the epf problem can be accomplished and we design a deterministic distributed algorithm that solves the problem for all configurations but those identified as unsolvable. Our approach is also characterized by the use of logical predicates in order to formally describe our algorithm as well as its correctness.

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previous chapter Towards a Universal Approach for Monotonic Searchability in Self-stabilizing Overlay Networks

next chapter Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model

The existence of such robots is guaranteed by the fact that the initial configuration was solvable, and hence by Lemma 3 there were no axes with only fixed-points. Moreover, the moves performed from the initial configuration until the current step guarantee to not create such kind of axes.

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Title: Asynchronous Embedded Pattern Formation Without Orientation
Authors: Serafino Cicerone
Gabriele Di Stefano
Alfredo Navarra
Publisher: Springer Berlin Heidelberg
Book: Distributed Computing
Print ISBN: 978-3-662-53425-0

Electronic ISBN: 978-3-662-53426-7

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-662-53426-7_7

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