Parallel Solution to the Dominating Set Problem by Tile Assembly System

Abstract

Abstract:The dominating set problem is a well known NP hard problem. It means that as the instance size grows, they quickly become impossible to solve on traditional digital computers. Tile assembly model has been demonstrated as a highly distributed parallel model of computation. Algorithmic tile assembly has been proved to be Turing-universal. This paper proposes a tile assembly system for the dominating set problem. It only needs Θ (mn) tile types to solve such a complex problem in the time Θ (m + n) where n and m are the number of vertices and edges of the given graph, respectively.