Grishanovich T. Efficient algorithms for arithmetic graphs

The dissertation investigates the numerical graphs and efficient algorithms for them. The theoretical question of complexity theory of algorithms. We consider those subclasses numerical graphs as arithmetic graphs. Shown the relevance of the development of algorithms for numeric columns. For such graphs have been developed and implemented in a programming language a new algorithm for decomposition of graphs by their vertices - graphs decomposition algorithm using their skeletons. We show that this algorithm provides greater efficiency in time for traditional ways to present graphs, and for natural arithmetic graphs. The article is adapted these algorithms for finding Hamiltonian cycles in graphs for numerical graphs: the return of the algorithm, Approx-TSP (G), the algorithm of polynomial time. Investigated the characteristics of such algorithms. It is shown that the number of columns can improve the evaluation time complexity of algorithms. Construct software in a visual programming environment that allows you to decompose a graph decomposition algorithm developed provided that the graph as adjacency matrix and natural arithmetic graph. And also makes finding Hamiltonian cycles in arithmetic graphs using adapted algorithms.