Optimal Geometric Partitions, Covers and K-Centers

Mugurel Ionut Andreica (1) , Eliana-Dina Tirsa (1) , Cristina Teodora Andreica (2) , Romulus Andreica (2) , Mihai Aristotel Ungureanu (3)

1 Parallel and Distributed Systems Laboratory [Bucarest]
2 Management and Finances Center
3 Internal and International Commercial and Financial-Banking Relations Dept.

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.

Mots clés: polygon partition; point cover; interval cover; rectangle cover; interval K-center; dynamic programming

Domaines: Algorithme et structure de données [cs.DS]; Géométrie algorithmique [cs.CG]

Mugurel Ionut Andreica, Eliana-Dina Tirsa, Cristina Teodora Andreica, Romulus Andreica, Mihai Aristotel Ungureanu. Optimal Geometric Partitions, Covers and K-Centers. Proceedings of the 9th WSEAS International Conference on Mathematics and Computers in Business and Economics (MCBE) (ISBN: 978-960-6766-76-3 / ISSN: 1790-5109), Jun 2008, Bucharest, Romania. pp.173-178. ⟨hal-00466868⟩