Mikhail Yu. Khachay

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It is known that the minimum affine separating committee (MASC) combinatorial optimization problem, which is related to some machine learning techniques, is NP-hard and does not belong to Apx class unless P = NP. In this paper, it is shown that the MASC problem formulated in a fixed dimension space within n > 1 is intractable even if sets defining an(More)
Two special cases of the Minimum Committee Problem are studied, the Minimum Committee Problem of Finite Sets (MCFS) and the Minimum Committee Problem of a System of Linear Inequalities(MCLE). It is known that the first of these problems is N P-hard (see [1]). In this paper we show the N P-hardness of two integer optimization problems connected with it. In(More)
The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well known Traveling Salesman Problem (TSP), where along with a weighted graph G = (V, E, w) we are given by a partition of its node set V = V1 ∪. .. ∪ V k into disjunctive subsets or clusters. The goal is to find a minimum cost cycle such that each cluster is hit by exactly one(More)
We consider the minimum affine separating committee (MASC) combinatorial optimization problem, which is related to ensemble machine learning techniques on the class of linear weak classifiers combined by the rule of simple majority. Actually, the MASC problem is a mathematical formalization of the famous Vapnik–Chervonenkis principle of structural risk(More)
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