Efficient Permutation-Based Range-Join Algorithms on N-Dimensional Meshes

ÐIn this paper, we present four efficient parallel algorithms for computing a nonequijoin, called range-join, of two relations on N-dimensional mesh-connected computers. Range-joins of relations R and S are an important generalization of conventional equijoins and band-joins and are solved by permutation-based approaches in all proposed algorithms. In general, after sorting all subsets of both relations, the proposed algorithms permute every sorted subset of relation S to each processor in turn, where it is joined with the local subset of relation R. To permute the subsets of S efficiently, we propose two data permutation approaches, namely, the shifting approach which permutes the data recursively from lower dimensions to higher dimensions and the Hamiltonian-cycle approach which first constructs a Hamiltonian cycle on the mesh and then permutes the data along this cycle by repeatedly transferring data from each processor to its successor. We apply the shifting approach to meshes with different storage capacities which results in two different join algorithms. The Basic Shifting Join (BASHJ) algorithm can minimize the number of subsets stored temporarily at a processor, but requires a large number of data transmissions, while the Buffering Shifting Join (BUSHJ) algorithm can achieve a high parallelism and minimize the number of data transmissions, but requires a large number of subsets stored at each processor. For constructing a Hamiltonian cycle on a mesh, we propose two different methods which also result in two different join algorithms. The Recursive Hamiltonian-Cycle Join (REHCJ) algorithm uses a single processor to construct a Hamiltonian cycle recursively, while the Parallel Hamiltonian-Cycle Join (PAHCJ) algorithm uses all processors to construct a Hamiltonian cycle in parallel. We analyze and compare these algorithms. The results shows that both Hamiltonian cycle algorithms require less storage and local join operations than the shifting algorithms, but more data movement steps.