1 research outputs found
Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach
Given any multiset F of points in the Euclidean plane and a set R of robots
such that |R|=|F|, the Arbitrary Pattern Formation (APF) problem asks for a
distributed algorithm that moves robots so as to reach a configuration similar
to F. Similarity means that robots must be disposed as F regardless of
translations, rotations, reflections, uniform scalings. Initially, each robot
occupies a distinct position. When active, a robot operates in standard LCM
cycles. Robots are asynchronous, oblivious, anonymous, silent and execute the
same distributed algorithm. So far, the problem has been mainly addressed by
assuming chirality, that is robots share a common left-right orientation. We
are interested in removing such a restriction. While working on the subject, we
faced several issues that required close attention. We deeply investigated how
such difficulties were overcome in the literature, revealing that crucial
arguments for the correctness proof of the existing algorithms have been
neglected. The systematic lack of rigorous arguments with respect to necessary
conditions required for providing correctness proofs deeply affects the
validity as well as the relevance of strategies proposed in the literature.
Here we design a new deterministic distributed algorithm that fully
characterizes APF showing its equivalence with the well-known Leader Election
problem in the asynchronous model without chirality. Our approach is
characterized by the use of logical predicates in order to formally describe
our algorithm as well as its correctness. In addition to the relevance of our
achievements, our techniques might help in revising previous results. In fact,
it comes out that well-established results like [Fujinaga et al, SIAM J. Comp.
44(3) 2015], more recent approaches like [Bramas et al, PODC and SSS 2016] and
'unofficial' results like [Dieudonne et al, arXiv:0902.2851] revealed to be not
correct.Comment: To appear in Distributed Computin