Range search in parallel using distributed data structures

The range search problem involves obtaining a set of data points (tuples, records) satisfying a query which specifies a range of values on each dimension, (attribute) of the data. A parallel algorithm for range searching is developed, using the concept of distributed data structures. The range tree proposed by J.L. Bentley (1980) is used as the data structure to be distributed. It is shown that O(log n) search time can be effected for a range search on n three-dimensional points using (2.log²n-10.logn +12) processors, and thus is optimal for the range tree distribution. The authors present a nontrivial implementation technique on the hypercube parallel architecture with which the above time and processor bound can be achieved without any communication overhead. The algorithm can easily be generalized for the case of d-dimensional range search