Sublinear geometric algorithms

Authors:
Bernard Chazelle;Ding Liu;Avner Magen
Affiliations:
Princeton University;Princeton University;University of Toronto
Venue:
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Year:
2003

Citing 17
Cited 15

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Improved algorithms for quantum identification of boolean oracles

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Abstract

We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons and polyhedra, point location in two-dimensional Delaunay triangulations and Voronoi diagrams, and ray shooting in convex polyhedra, all of which run in time O(√n), where n is the size of the input. We also provide sublinear solutions for the approximate evaluation of the volume of a convex polytope and the length of the shortest path between two points on the boundary.