Navigating nets: simple algorithms for proximity search

d Abstract] Robert Krauthgamer James R. Lee We present a simple deterministic data structure for maintaining a set S of points in a general metric space, while supporting proximity search (nearest neighbor and range queries) and updates to S (insertions and deletions). Our data structure consists of a sequence of progressively finer -nets of S, with pointers that allow us to navigate easily from one scale to the next. We analyze the worst-case complexity of this data e in terms of the "abstract dimensionality" of the metric S. Our data structure is extremely efficient for metrics of bounded dimension and is essentially optimal in a certain model of distance computation. Finally, as a special case, our approach improves over one recently devised by Karger and Ruhl [KR02].

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Robert Krauthgamer, James R. Lee
• Keywords: Algorithms, Data Structure, Deterministic Data Structure, General Metric Space, SODA 2004