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Navigating nets: simple algorithms for proximity search

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 ε-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 structure 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].