The subset sum problem is to find subsets in a given number set, meanwhile number sum of the subset is equal to appointed value. It is a classical NP-complete problem in graph theory. It can be solved by the electronic computer in exponential time. In this paper, we consider a DNA procedure for solving the subset sum problem in the Adleman-Lipton model. The procedure works in O(n) steps for the subset sum problem of an undirected graph with n vertices. The innovation of the procedure is the ingenious choice of the vertices strands’ length, which can get the solution of the problem in proper length range and simultaneity simplify the complexity of the computation.
Li, Lei; Zhao, Kai; and Ji, Zuwen
"A Genetic Algorithm to Solve the Subset Sum Problem based on Parallel Computing,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 41.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss2/41