A note on the nearest neighbor in growth-restricted metrics

In this paper, we give results relevant to sequential and distributed dynamic data structures for finding nearest neighbors in growth-restricted metrics. Our sequential data structure uses linear space, and requires O(log n) queries in expecation and O(log n) queries for lookups with high probability. This improves the results of Karger and Ruhl [4], whose data structure uses O(n log n) space with comparable expected time bounds. This also improves on the time bound of a load-balanced version of algorithm (for dynamic networks) presented in [3]. Our algorithm was inspired by the object location data structure developed by Plaxton, Rajaraman and Richa [6], and is similar in structure to the algorithm of Krauthgamer and Lee [5]. It is significantly different that of Karger and Ruhl [4]. A distributed version of the algorithm presented here is in use as a part of Tapestry [3, 8], a peer-topeer object location system based on [6].

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Kirsten Hildrum, John Kubiatowicz, Sean Ma, Satish Rao
• Keywords: Algorithms, Data Structure, Data Structure Uses, SODA 2004, Time Bound