Matrix algorithm of solving graph cutting problem

Matrix algorithm of solving graph cutting problem has been suggested. The main algorithm points based on matrix graph presentation were considered. Formalization of the main algorithm procedures - defining estimations for selecting relocatable matrix elements and matrix conversion by reciprocal transfer of columns and lines was given. Algorithm operation was considered by the example of data transmission graph between the stations of local computer system networ

A solution to the problem of clustered objects compact partitioning

The urgency of the study consists in the fact that an object arrangement topology of a distributed system is often nonuniform. Objects can be placed at different distances from each other, thus forming clusters. That is why solving the problem of compact partitioning into sets containing thousands of objects requires the most effective way to a better use of natural structuring of objects that form clusters. The aim of the study is the development of methods of compact partitioning of sets of objects presented as clusters. The research methods are based on applied theories of sets, theory of compact sets and compact partitions, and linear programming methods with Boolean variables. As a result, the paper offers the method necessary to analyze composition and content of clusters. It also evaluates cluster compactness, which results in the decision to include clusters into the sets of partitions. It addresses the problem of optimizing the rearrangement of objects between compact sets that form clusters, which is based on the criteria of maximizing the total compactness of sets. The problem is formulated in the class of objectives of linear programming methods with Boolean variables. It introduces the example of object rearrangement

Software for storage and processing coded messages for the international exchange of meteorological information

The approach allows representing data of international codes for exchange of meteorological information using metadescription as the formalism associated with certain categories of resources. Development of metadata components was based on an analysis of the data of surface meteorological observations, atmosphere vertical sounding, atmosphere wind sounding, weather radar observing, observations from satellites and others. A common set of metadata components was formed including classes, divisions and groups for a generalized description of the meteorological data. The structure and content of the main components of a generalized metadescription are presented in detail by the example of representation of meteorological observations from land and sea stations. The functional structure of a distributed computing system is described. It allows organizing the storage of large volumes of meteorological data for their further processing in the solution of problems of the analysis and forecasting of climatic processes

Polynomial algorithm of computing complete graph invariant on the basis of integral structure descriptor

The relevance of the research is caused by the unsolved problem of searching for the complete graph invariant and polynomial algorithm for its computing. The aim of the research is in determining the complete invariant of an ordinary graph on the basis of integral descriptor of abstract structure and in developing the efficient algorithm for computing the complete invariant. The techniques of the research are based on the graph theory and the theory of structural differences code integration in abstract graph structures. The authors have proposed the algorithm for solving one of the most complex problems of graph theory. It is the computation of complete graph invariant. The algorithm is based on the methods of free and dependent integration of structural differences codes in a graph; it is characterized by simplicity, efficiency and it has polynomial estimation of the limiting amount of computation. The complete invariant is represented in the form of a vector of integral descriptor for graph abstract structure vertices and contains information for forming isomorphism substitution. Using Java the GraphISD software was developed implementing the proposed algorithm. The paper introduces the examples of computing the complete invariants at free and dependent integration

Polynomiality of method for computing graph structure integral descriptor

The relevance of the research is caused by the necessity of developing the efficient method of invariant description and analysis of abstract structures of graph models. The aim of the research is to substantiate the polinomiality of the method for computing the integral descriptor of graph abstract structure proposed by the authors. The research techniques are based on application of machinery of graph theory and methods of free and dependent integration of codes of graph structural differences. The authors have introduced the notion of stable group of vertices in graph and stated the conditions of occurrence and existence of such groups at integration of structural differences codes when computing the integral structure descriptor. A number of features which disclose the appropriateness of application of the main rules of the integral structure descriptor and its polinomiality was determined for stable groups. It was ascertained on the basis of the defined features that the conditions for stable group existing are conditioned by hard limits; the vertices of different stable groups can not generate new stable groups. The authors have also defined the factor of full isolation of stable groups that predetermined considerably the efficiency of algorithm for computing the full graph structure descriptor. Polinomiality of the technique is demonstrated for the most complex case when graphs are homogeneous and contain stable groups. The authors developed Java GraphISD software for the experimental investigations of integral structure descriptor technique and introduced the results of its operation

Polynomiality of method for computing graph structure integral descriptor

The relevance of the research is caused by the necessity of developing the efficient method of invariant description and analysis of abstract structures of graph models. The aim of the research is to substantiate the polinomiality of the method for computing the integral descriptor of graph abstract structure proposed by the authors. The research techniques are based on application of machinery of graph theory and methods of free and dependent integration of codes of graph structural differences. The authors have introduced the notion of stable group of vertices in graph and stated the conditions of occurrence and existence of such groups at integration of structural differences codes when computing the integral structure descriptor. A number of features which disclose the appropriateness of application of the main rules of the integral structure descriptor and its polinomiality was determined for stable groups. It was ascertained on the basis of the defined features that the conditions for stable group existing are conditioned by hard limits; the vertices of different stable groups can not generate new stable groups. The authors have also defined the factor of full isolation of stable groups that predetermined considerably the efficiency of algorithm for computing the full graph structure descriptor. Polinomiality of the technique is demonstrated for the most complex case when graphs are homogeneous and contain stable groups. The authors developed Java GraphISD software for the experimental investigations of integral structure descriptor technique and introduced the results of its operation

Polynomial algorithm of computing complete graph invariant on the basis of integral structure descriptor

The relevance of the research is caused by the unsolved problem of searching for the complete graph invariant and polynomial algorithm for its computing. The aim of the research is in determining the complete invariant of an ordinary graph on the basis of integral descriptor of abstract structure and in developing the efficient algorithm for computing the complete invariant. The techniques of the research are based on the graph theory and the theory of structural differences code integration in abstract graph structures. The authors have proposed the algorithm for solving one of the most complex problems of graph theory. It is the computation of complete graph invariant. The algorithm is based on the methods of free and dependent integration of structural differences codes in a graph; it is characterized by simplicity, efficiency and it has polynomial estimation of the limiting amount of computation. The complete invariant is represented in the form of a vector of integral descriptor for graph abstract structure vertices and contains information for forming isomorphism substitution. Using Java the GraphISD software was developed implementing the proposed algorithm. The paper introduces the examples of computing the complete invariants at free and dependent integration