Optimal and suboptimal robust algorithms for proximity graphs

Authors:
Ferran Hurtado;Giuseppe Liotta;Henk Meijer
Affiliations:
Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli studi di Perugia, Via Duranti, 06125 Perugia, Italy;Department of Computing and Information Science Queen's Univ., Kingston, Ontario, Canada
Venue:
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Year:
2003

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Abstract

Given a set of n points in the plane, any β-skeleton and [γ0, γ1]-graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γ0, γ1] values that result, in non-planar graphs. We show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n2) time.