Parallel load balancing for problems with good bisectors

Parallel load balancing is studied for problems with certain bisection properties. A class of problems has α-bisectors if every problem p of weight w(p) in the class can be subdivided into two subproblems whose weight (load) is at least an a-fraction of the original problem. A problem p is to be split into N subproblems such that the maximum weight among them is as close to w(p)/N as possible. It was previously known that good load balancing can be achieved for such classes of problems using Algorithm HF, a sequential algorithm that repeatedly bisects the subproblem with maximum weight. Several parallel variants of Algorithm HF are introduced and analyzed with respect to worst-case load imbalance, running-time, and communication overhead. For fixed α, all variants have running-time O(log N) and provide constant upper bounds on the worst-case load imbalance. Results of simulation experiments regarding the load balance achieved in the average case are presented