An efficient permutation-based parallel algorithm for range-join in hypercubes

Abstract

The range-join of sets R and S is defined to be the set containing all tuples (r, s) that satisfy e, I 1 r -s I I e2 where r E R, s ES, e, and e2 are fixed constants. This paper proposes an efficient parallel range-join algorithm in hypercubes. To compute the range-join of two sets R and S on a hypercube of p processors (p I I R 1 = m I I S 1 = n), the proposed algorithm simply permutes the elements of R to obtain their possible combinations with the elements of S and thus all possible local range-joins. Requiring only O((m + n)/p) local memory at each processor, our algorithm has a time complexity O(((n/p) + m) log(n/p)) in the best case when no element in S matches any element in R; O(T,k,,, + (m/p)) in the worst case when all elements in S match each element in R, where Tk SDr, = O(k log k) when all elements in S are distinct, and T&, = O(k) when all elements in S are equal, k = n/p. The general-case time complexity of the algorithm is also shown.