Using Central Nodes to Improve P System Synchronization

Abstract

We present an improved solution for the Firing Squad Synchronization Problem (FSSP) for digraph-based P systems. We improve our previous FSSP algorithm by allowing the general to delegate a more central cell in the P system to send the nal command to synchronize. With e being the eccentricity of the general and r denoting the radius of the underlying digraph, our new algorithm guarantees to synchronize all cells of the system, between e + 2r + 3 steps (for all trees structures and many digraphs) and up to 3e + 7 steps, in the worst case for any digraph. Empirical results show our new algorithm for tree-based P systems yields at least 20% reduction in the number of steps needed to synchronize over the previous best-known algorithm.