Generalized FSSP on Hexagonal Tiling: Towards Arbitrary Regular Spaces

Abstract

Here we present a solution to the generalized firing squad synchronization problem that works on some class of shapes in the hexagonal tiling of the plane. The solution is obtained from a previous solution which works on grids with either a von Neumann or a Moore neighborhood. Analyzing the construction of this previous solution, we were able to exhibit a parameter that leads us to abstract the solution. First, and for an arbitrary considered neighborhood, we focus our attention on a class of shapes built from this neighborhood, and determine the corresponding parameter value for them. Second, we apply our previous solution with the determined parameter value for the hexagonal neighborhood and show that, indeed, all the considered shapes on the hexagonal tiling synchronizes.