Generating Tree Decomposition of Graphs with Imperialist Competitive Algorithm for Use in Secret Sharing Scheme

Secret sharing refers to methods of distributing a secret amongst a group of participants, each of whom is assigned with a share of the secret. The secret can be reconstructed only when a sufficient number, of possibly different types of shares are combined together. Different secret sharing methods have been      presented, such as secret sharing schemes based on dominating set and edge dominating set. In edge     dominating set method, it is required that all of the edge dominating sets are obtained for the graph, which is a NP-complete problem. All of the edge dominating sets can be easily obtained, using tree decomposition of the graph and dynamic programming. Although generating tree decomposition of a graph with finite treewidth can be solved in polynomial time, but it is shown to be NP-complete for general graphs. In this paper, to generate tree decompositions of general graphs, we use the notion of Imperialist Competitive   Algorithm (ICA) which can be applied in parallel. Therefore, the proposed method, in addition to being a new method for implementation of the secret sharing scheme, can reduce runtime by up to five percent in parallel.