Aggregate-Max Nearest Neighbor Searching in the Plane
Haitao Wang

TL;DR
This paper introduces efficient data structures for aggregate maximum nearest neighbor queries in the plane under L1 and L2 distances, improving upon previous heuristics and approximations.
Contribution
It presents novel exact data structures for MAX nearest neighbor queries with optimal or near-optimal complexities for both L1 and L2 metrics.
Findings
L1 data structure answers queries in O(m+log n) time
L2 data structure achieves O(m√n log^O(1) n) query time
Top-k queries are answered efficiently with O(n) space and O(n log n) preprocessing
Abstract
We study the aggregate/group nearest neighbor searching for the MAX operator in the plane. For a set of points and a query set of points, the query asks for a point of whose maximum distance to the points in is minimized. We present data structures for answering such queries for both and distance measures. Previously, only heuristic and approximation algorithms were given for both versions. For the version, we build a data structure of O(n) size in time, such that each query can be answered in time. For the version, we build a data structure in time and space, such that each query can be answered in time, and alternatively, we build a data structure in time and space for any , such that each query can be answered in…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Data Management and Algorithms · Digital Image Processing Techniques
