General Preex Computations on Enhanced Meshes, with Applications

In this paper we present two eecient algorithms for general preex computations (GPC, for sort) on meshes with multiple broadcasting and reconngurable meshes respectively. On a mesh with multiple broadcasting of size n n, the GPC problem of size kn (1 k n) can be solved in O(log n) time if k = 1, and in O(k log n log k) time if 2 k n. On a reconngurable mesh of size n n, the GPC problem of size kn (1 k n) can be solved in O(t(n)k) time. Here t(n) is the time used to compute the product of p n elements on a reconngurable mesh of size p n p n, which is a constant in many practical situations. Our algorithms can be applied to solve a number of problems in computational geometry , graph theory, and combinatorics on enhanced meshes. Speciically, we show that the sorting, ANSV, maximal points, ECDF searching, and two-set dominance counting problems of size kn (1 k n) can be solved in O(k) time on a reconngurable mesh of size n n.