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The article proposes the implicit exhaustive search procedure based on the triangle decomposition of graphs for determining the maximal clique in the arbitrary undirected graph G in polynomial time; it has allowed developing an exact algorithm for solving the problem with time complexity not exceeding ) ( 7 n O , where n is the number of vertices in the graph G.Index Terms-Мaximal independent set, click, vertex cover, decomposition of a graph into triangles 2 An Approach to Determination of Maximal Cliques in Undirected Graphs

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The article describes the scheduling system for heterogeneous distributed computing systems. The scheduler based on minimal cover method. The analysis of the effectiveness of the scheduling system for tasks with varying intensity, the law of distribution complexity. The advantage of the method of minimal cover compared to FCFS. A system of rules for the optimization of the proposed planning changes in the intensity and complexity of tasks.