Linear Time Approximation Schemes for Geometric Maximum Coverage
Abstract
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P covered by these rectangles is maximized.For any fixed > 0, we present efficient approximation schemes that can find (1-{\epsilon})-approximation to the optimal solution.In particular, for m = 1, our algorithm runs in linear time O(n log( 1/{\epsilon})), improving over the previous result. For m > 1, we present an algorithm that runs in O(n/{\epsilon}log(1/{\epsilon})+m(1/{\epsilon})^(O(min(sqrt(m),1/{\epsilon}))) time.
Cite
@article{arxiv.1505.02591,
title = {Linear Time Approximation Schemes for Geometric Maximum Coverage},
author = {Jian Li and Haitao Wang and Bowei Zhang and Ningye Zhang},
journal= {arXiv preprint arXiv:1505.02591},
year = {2015}
}
Comments
17 pages, 4 figures, to be published in the Proceedings of 21st International Computing and Combinatorics Conference(COCOON2015)