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- Mikhail Yu. Khachay, Maria Poberii
- Informatica, Lith. Acad. Sci.
- 2009

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)

- Mikhail Yu. Khachay, Roman Dubinin
- DOOR
- 2016

- Mikhail Yu. Khachay
- J. Math. Model. Algorithms
- 2007

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)

- Mikhail Yu. Khachay, Katherine Neznakhina
- J. Global Optimization
- 2016

- Dmitry I. Ignatov, Mikhail Yu. Khachay, +4 authors Boris Mirkin
- 2014

The proceedings are published online on the CEUR-Workshop web site in a series with ISSN 1613-0073, Vol-1197. Preface This volume contains supplementary proceedings of the third conference on Analysis of Images, Social Networks, and Texts (AIST'2014). The first two conferences in 2012 and 2013 attracted a significant number of students, researchers,… (More)

- Alexander Dremin, Mikhail Yu. Khachay, Anton Leshko
- AIST
- 2014

- Mikhail Yu. Khachay, Helen Zaytseva
- COCOA
- 2015

- Mikhail Yu. Khachay
- Machine Learning
- 2015

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)

- Mikhail Yu. Khachay, Katherine Neznakhina
- DOOR
- 2016

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)

- Mikhail Yu. Khachay, Maxim Pasynkov
- AIST
- 2015