Simulating the Bitonic Sort on a 2D-mesh with P Systems

Abstract

This paper gives a version of the parallel bitonic sorting algorithm of Batcher, which can sort N elements in time O(log2 N). When applying it to the 2D mesh architecture, two indexing functions are considered, row-major and shuffled row- major. Some properties are proved for the later, together with a correctness proof of the proposed algorithm. Two simulations with P systems are proposed and discussed. The first one uses dynamic communication graphs and follows the guidelines of the mesh version of the algorithm. The second simulation requires only symbol rewriting rules in one membrane.