Complexity and Approximability of Committee Polyhedral Separability of Sets in General Position

Authors:
Michael Khachay;Maria Poberii
Affiliations:
-;Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S.Kovalevskoy 16, 620219 Ekaterinburg, Russia, e-mail: mkhachay@imm.uran.ru
Venue:
Informatica
Year:
2009

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Abstract

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 n1 is intractable even if sets defining an instance of the problem are in general position. A new polynomial-time approximation algorithm for this modification of the MASC problem is presented. An approximation ratio and complexity bounds of the algorithm are obtained.