Different time solutions for the firing squad synchronization problem on basic grid networks

¹ Faculty of Informatics, Masaryk University, Brno, Czech Republic.
² Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi di Salerno, Italia.

Abstract

We present several solutions to the Firing Squad Synchronization Problem on grid networks of different shapes. The nodes are finite state processors that work in unison with other processors and in synchronized discrete steps. The networks we deal with are: the line, the ring and the square. For all of these models we consider one- and two-way communication modes and we also constrain the quantity of information that adjacent processors can exchange at each step. We first present synchronization algorithms that work in time n², nlogn, , 2ⁿ, where n is a total number of processors. Synchronization methods are described through so called signals that are then used as building blocks to compose synchronization solutions for the cases that synchronization times are expressed by polynomials with nonnegative coefficients.