# Efficient NC Algorithms for Set Cover with Applications to Learning and Geometry

@article{Berger1994EfficientNA, title={Efficient NC Algorithms for Set Cover with Applications to Learning and Geometry}, author={Bonnie Berger and John Rompel and Peter W. Shor}, journal={J. Comput. Syst. Sci.}, year={1994}, volume={49}, pages={454-477} }

- Published 1994 in J. Comput. Syst. Sci.
DOI:10.1016/S0022-0000(05)80068-6

In this paper we give the first NC approximation algorithms for the unweighted and weighted set cover problems. Our algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/weight, thus matching the performance of the best sequential algorithms. We apply our set cover algorithm to learning theory, giving an NC algorithm to learn the concept class obtained by taking the closure under finite union or finite intersection of any concept class of… CONTINUE READING