Optimal Line Bipartitions of Point Sets - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue International Journal of Computational Geometry and Applications Année : 1999

Optimal Line Bipartitions of Point Sets

Résumé

Let 5 be a set of n points in the plane. We study the following problem: Partition S by a line into two subsets Sa and St, such that max{f(Sa), f(Sb)} is minimal, where / is any monotone function defined over 2^S. We first present a solution to the case where the points in S are the vertices of a convex polygon and apply it to some common cases -- f(S') is the perimeter, area, or width of the convex hull of S* C S -- to obtain linear solutions (or 0(n log n) solutions if the convex hull of S is not given) to the corresponding problems. This solution is based on an efficient procedure for finding a minimal entry in matrices of some special type, which we believe is of independent interest. For the general case we present a linear space solution which is in some sense output sensitive. It yields solutions to the perimeter and area cases that are never slower and often faster than the best previous solutions.

Dates et versions

hal-00795067 , version 1 (27-02-2013)

Identifiants

Citer

Olivier Devillers, Matthew J. Katz. Optimal Line Bipartitions of Point Sets. International Journal of Computational Geometry and Applications, 1999, 9 (1), pp.39-51. ⟨10.1142/S0218195999000042⟩. ⟨hal-00795067⟩
44 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More