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 needsQ(mn) tile types to solve such a complex problem in the timeQ(m+n) where n and m are the number of vertices and edges of the given graph, respectively.
Digital Object Identifier (DOI)
Zheng, Hongjiang; Huang, Yufang; Xiao, Jianhua; Liu, Jian; and Song, Tao
"Parallel Solution to the Dominating Set Problem by Tile Assembly System,"
Applied Mathematics & Information Sciences: Vol. 08:
1, Article 43.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss1/43