Generalized class cover problem with Axis-Parallel strips

Abstract

We initiate the study of a generalization of the class cover problem [1, 2], the generalized class cover problem, where we are allowed to misclassify some points provided we pay an associated positive penalty for every misclassified point. We study five different variants of generalized class cover problem with axis-parallel strips and half-strips in the plane, thus extending similar work by Bereg et al. [2] on the class cover problem. For each of these variants, we either show that they are in P, or prove that they are NP-complete and give constant factor approximation algorithms