Towards in-place geometric algorithms and data structures

For many geometric problems, there are efficient algorithms that use surprisingly very little extra space other than the given array holding the input. For many geometric query problems, there are efficient data structures that need no extra space at all other than an array holding a permutation of the input. In this paper, we obtain the first such space-economical solutions for a number of fundamental problems, including three-dimensional convex hull and two-dimensional Delaunay triangulation computations, as well as fixed-dimensional range queries and fixed-dimensional nearest neighbor queries.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Hervé Brönnimann, Timothy M. Chan, Eric Y. Chen
• Keywords: COMPGEOM 2004, Extra Space, Geometric Query Problems, Little Extra Space