Randomized Static Load Balancing for Tree-Shaped Computations

Parallelizing a problem by statically assigning a xed number of subprob-lems to each processor is very popular due to its simplicity and low communication overhead. In many cases it can be proved to be suucient to randomly assign O(log N) subproblems to each of N processors in order to smooth out load imbalance due to varying subproblem sizes. However, this is not true for the tree structured computations considered in this paper because the subproblem sizes get less uniform when the number of generated subproblems is increased. Even under moderate assumptions, a polynomial number of subproblems needs to be assigned to each processor. Still, for machines with slow communication and applications with good splitting functions, a carefully designed randomized static load balancer can be a competitive alternative to dynamic load balancing schemes. The results also help to explain the impact of static load balancing as an initialization method for a subsequent dynamic load balancing phase.