Approximation Algorithms for the Class Cover Problem

Authors:
Adam H. Cannon;Lenore J. Cowen
Affiliations:
Department of Computer Science, Columbia University, 1214 Amsterdam Avenue, MC 0401, New York, NY 10027, USA E-mail: cannon@cs.columbia.edu;Department of Computer Science, Tufts University, Halligan Hall, 161 College Avenue, Medford, MA 02140, USA E-mail: cowen@cs.tufts.edu
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2004

Citing 5
Cited 9

Introduction to algorithms

Introduction to algorithms
Approximation schemes for covering and packing problems in image processing and VLSI

Journal of the ACM (JACM)
Hardness of approximations

Approximation algorithms for NP-hard problems
Regular Article: Randomized Nonlinear Projections Uncover High-Dimensional Structure

Advances in Applied Mathematics
On the hardness of approximating minimization problems

Journal of the ACM (JACM)

A new family of proximity graphs: class cover catch digraphs

Discrete Applied Mathematics
Convex sets as prototypes for classifying patterns

Engineering Applications of Artificial Intelligence
A randomized sphere cover classifier

IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
A hybrid algorithm for solving generalized class cover problem

ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
A fuzzy neural network system based on generalized class cover problem

FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part I
The convex subclass method: combinatorial classifier based on a family of convex sets

MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
A fuzzy neural network system based on generalized class cover and particle swarm optimization

ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part II
The class cover problem with boxes

Computational Geometry: Theory and Applications
Computing optimal islands

Operations Research Letters

Quantified Score

Hi-index	0.01

Visualization

Abstract

We introduce the class cover problem, a variant of disk cover with forbidden regions, with applications to classification and facility location problems. We prove similar hardness results to disk cover. We then present a polynomial-time approximation algorithm for class cover that performs within a ln n+1 factor of optimal, which is nearly tight under standard hardness assumptions. In the special case that the points lie in a d-dimensional space with Euclidean norm, for some fixed constant d, we obtain a polynomial time approximation scheme.