In this paper we present some new, practical, geometric optimization techniques for computing polygon partitions, 1D and 2D point, interval, square and rectangle covers, as well as 1D and 2D interval and rectangle K-centers. All the techniques we present have immediate applications to several cost optimization and facility location problems which are quite common in practice. The main technique employed is dynamic programming, but we also make use of efficient data structures and fast greedy algorithms.
Extended version of the paper with the same title, published in Proceedings of the 9th WSEAS International Conference on Mathematics and Computers in Business and Economics, pp. 173-178, Bucharest, Romania, 24-26 June 2008.