Algorithmic tile self-assembly model for the minimum dominating set problem

Abstract

Self-assembly is the process in which simple components can spontaneously form complex complexes. This field has produced a formal model of self-assembly known as the tile self-assembly model. Recently, computation by this model is proved to be a promising technique in nanotechnology. In this paper, aiming to the minimum dominating set problem which is NP-complete, how the tile self-assembly model is used to implement this problem is shown including nondeterministic guess operation, assigning operation and logic OR operation. This method can be successfully performed this problem in Θ(n 2) steps. Here n is the number of vertices of the given graph in the minimum dominating set problem. © 2013 Springer.