Optimal geometric partitions, covers and K-centers

Authors:
Mugurel Ionut Andreica;Eliana-Dina Tirsa;Cristina Teodora Andreica;Romulus Andreica;Mihai Aristotel Ungureanu
Affiliations:
Politehnica University of Bucharest, Bucharest, Romania;Politehnica University of Bucharest, Bucharest, Romania;Commercial Academy Satu Mare, Satu Mare, Romania;Commercial Academy Satu Mare, Satu Mare, Romania;Romanian-American University, Bucharest, Romania
Venue:
MCBE'08 Proceedings of the 9th WSEAS International Conference on Mathematics & Computers In Business and Economics
Year:
2008

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Abstract

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.