Inferring a Union of Halfspaces from Examples

Authors:
Tatsuya Akutsu;Sascha Ott
Affiliations:
-;-
Venue:
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Year:
2002

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Abstract

We consider the following problem which is motivated by applications in Bioinformatics: given positive and negative points in d- dimensions, find a minimum cardinality set of halfspaces whose union covers all positive points and no negative points. We prove that approximation of this problem is at least as hard as approximation of graph coloring. On the other hand, we show that the two-dimensional case of the problem can be solved in polynomial time. Other related results are shown, too.