Arbitrary Pattern Formation on Infinite Regular Tessellation Graphs [article]

Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano, Alfredo Navarra
2020 arXiv   pre-print
Given a set R of robots, each one located at different vertices of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF) problem. Given a multiset F of grid vertices such that |R|=|F|, APF 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. So far, as possible graph discretizing the Euclidean plane only the
more » ... andard square grid has been considered in the context of the classical Look-Compute-Move model. However, it is natural to consider also the other regular tessellation graphs, that are triangular and hexagonal grids. We provide a resolution algorithm for APF when the initial configuration is asymmetric and the considered topology is any regular tessellation graph.
arXiv:2010.14152v1 fatcat:5qog6ryf5zdcbleyfck5s5t7gu