519.86Well-known optimization problems on graphs are considered under uncertainty when parameter domains are specified in the form of intervals. Exponential estimates of computational complexity of problems being studied and also problems that are polynomial in the classical formulation are substantiated. Polynomially solvable subclasses are found, and sufficient conditions of statistical efficiency of a proposed approximate algorithm are constructively substantiated.
A multicriteria choice problem is considered. It is proposed to solve this problem by requiring the solution to be invariant under a certain group of transformations. Groups of transformations of a linear space that preserve the Pareto order in this space are investigated. The maximum group of such transformations is calculated up to group isomorphism. The most interesting discrete and continuous subgroups of the Pareto group are considered.
The paper deals with the problem of prediction of time series with memory for which classical prediction methods are frequently inadequate. A method is proposed that is based on a model of cellular automata, classification methods, and fuzzy set theory. The accuracy of models based on this method is estimated.
We study the connection between classifications on finite set and the problem of graph coloring. We consider the optimality criterion for classification of special type: h-classifications, which are built on the base of proximity measure. It is shown that the problem of finding the optimal h-classification can be reduced to the problem of coloring of non-adjacency graph vertices by the smallest possible number of colors. We consider algorithms of proper coloring of graph vertices.
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