Space-efficient approximate Voronoi diagrams

Given a set S of n points in IRd , a (t, )-approximate Voronoi diagram (AVD) is a partition of space into constant complexity cells, where each cell c is associated with t representative points of S, such that for any point in c, one of the associated representatives approximates the nearest neighbor to within a factor of (1 + ). Like the Voronoi diagram, this structure defines a spatial subdivision. It also has the desirable properties of being easy to construct and providing a simple and practical data structure for answering approximate nearest neighbor queries. The goal is to minimize the number and complexity of the cells in the AVD. We assume that the dimension d is fixed. Given a real parameter , where 2 1/, we show that it is possible to construct a (t, )-AVD consisting of O(n d-1 2 3(d-1) 2 log ) cells for t = O(1/()(d-1)/2 ). This yields a data structure of O(nd-1 log ) space (including the space for representatives) that can answer -NN queries in time O(log(n) + 1/()(d-1...

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Sunil Arya, Theocharis Malamatos, David M. Mount
• Keywords: -approximate Nearest Neighbor, Algorithms, Approximate Nearest Neighbor, Nearest Neighbor Queries, STOC 2002