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

The range-join of sets R and S is defined to be the set containing all tuples (r, s) that satisfy e₁ ≤ |r - s| ≤ e₂, where r ε{lunate} R, s ε{lunate} S, e₁, 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 ≤ |R| = m ≤ |S| = 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_sort + ( m p)) in the worst case when all elements in S match each element in R, where T^k_sort = O(k log k) when all elements in S are distinct, and T^k_sort = O(k) when all elements in S are equal, k = n p. The general-case time complexity of the algorithm is also shown.