Zahovalko Т. Research of problem of graph and hypergraph edge cover and development of effective algorithms for their resolving

The dissertation is devoted to the research of discrete optimization and vector problems of graph and hypergraph edge cover with standard subgraph. For the first time estimation of computing complexity of new problem setting on simple graph, bichromatic graph and hypergraph was obtained. Polynomial resolving subclass was singled out from classes of NP-complex and hard to resolve problems. The theory of mathematics modeling was given a further development by the theory of graphs and hypergraphs. New mathematics models were created: problem of land using was built for hypergraph and advertisement placement problem was found for grid graph. Effective resolving algorithms were developed for all the problems