Computational geometry: an introduction
Computational geometry: an introduction
Computing relative neighbourhood graphs in the plane
Pattern Recognition
Connection autonomy in SIMD computers: a VLSI implementation
Journal of Parallel and Distributed Computing
IEEE Transactions on Computers
Journal of Parallel and Distributed Computing
Parallel Computations on Reconfigurable Meshes
IEEE Transactions on Computers
Reconfigurable Buses with Shift Switching: Concepts and Applications
IEEE Transactions on Parallel and Distributed Systems
Time-optimal nearest-neighbor computations on enhanced meshes
Journal of Parallel and Distributed Computing
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
An Optimal Sorting Algorithm on Reconfigurable Mesh
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Group Nearest Neighbor Queries
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Aggregate nearest neighbor queries in spatial databases
ACM Transactions on Database Systems (TODS)
Two ellipse-based pruning methods for group nearest neighbor queries
Proceedings of the 13th annual ACM international workshop on Geographic information systems
Efficient difference NN queries for moving objects
APWeb/WAIM'07 Proceedings of the joint 9th Asia-Pacific web and 8th international conference on web-age information management conference on Advances in data and web management
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Given a set S of n points in the plane and two directions $r_1$ and $r_2,$ the Angle-Restricted All Nearest Neighbor problem (ARANN, for short) asks to compute, for every point p in S, the nearest point in S lying in the planar region bounded by two rays in the directions $r_1$ and $r_2$ emanating from p. The ARANN problem generalizes the well-known ANN problem and finds applications to pattern recognition, image processing, and computational morphology. Our main contribution is to present an algorithm that solves an instance of size n of the ARANN problem in O(1) time on a reconfigurable mesh of size n脳n. Our algorithm is optimal in the sense that $\Omega\;(n^2)$ processors are necessary to solve the ARANN problem in O(1) time. By using our ARANN algorithm, we can provide O(1) time solutions to the tasks of constructing the Geographic Neighborhood Graph and the Relative Neighborhood Graph of n points in the plane on a reconfigurable mesh of size n脳n. We also show that, on a somewhat stronger reconfigurable mesh of size $n\times n^2,$ the Euclidean Minimum Spanning Tree of n points can be computed in O(1) time.