Deterministic load balancing for parallel joins

We study the problem of distributing the tuples of a relation to a number of processors organized in an r-dimensional hypercube, which is an important task for parallel join processing. In contrast to previous work, which proposed randomized algorithms for the task, we ask here the question of how to construct efficient deterministic distribution strategies that can optimally load balance the input relation. We first present some general lower bounds on the load for any dimension; these bounds depend not only on the size of the relation, but also on the maximum frequency of each value in the relation. We then construct an algorithm for the case of 1 dimension that is optimal within a constant factor, and an algorithm for the case of 2 dimensions that is optimal within a polylogarithmic factor. Our 2-dimensional algorithm is based on an interesting connection with the vector load balancing problem, a well-studied problem that generalizes classic load balancing.