Parallel Range Searching in Large Databases Based on General Parallel Prefix Computation

General Preex Computation (GPC) problem has been shown to be the kernel routine that captures the hardest part of parallel algorithms in elds such as computer graphics, medical imaging, databases, and computational geometry. We present the rst computation and communication optimal algorithm on Coarse Grained Multicomputers (CGM) for solving GPC and, speciically, present its application on parallel range searching in large databases in the same computation and communication eecient manners. General Preex Computation (GPC, 3]) is a generic problem component that captures the most common, diicult kernel of many types of problems. The deenition is as follows : Let ff (1); f(2); ; f(n)g and fy(1); y(2); ; y(n)g be two sequences of elements with a binary associative operator deened on the f elements and a linear order deened on the y elements. It is required to compute the sequence fD(1); D(2); ; D(n)g whose elements D(m),m = 1; 2; ; n are deened as D(m) = f(j 1) f(j 2) f(j k), where j 1 < j 2 < < j k and fj 1 ; j 2 ; ; j k g is the sequence of indices such that j i < m and y(j i) y(m) for i = 1; 2; ; k.