Implementation of Maximum Independent Set Problem by Algorithmic Tile Self-Assembly

The maximum independent set problem is a classic combinational optimization problem. Recently, algorithmic tile self-assembly is considered as a promising technique in nanotechnology. In this work, we show how the tile self-assembly process is used to implement the maximum independent set problem including three small systems: nondeterministic guess system, AND operation system and comparing system. Our method can be successfully performed this problem in Θ(mn) steps parallely and at very low cost, here n and m is the number of vertices and edges of the given graph.