Load balancing on a hypercube

Assuming there is a hypercube with p=2^d processors and that each hypercube processor, PE(i), has L_i units of load. The load is always in integral units and may be distributed to other processors in integral units. In the load balancing problem the load is required to be redistributed so that if L´_i is the load on processor i following the redistribution, then |L´_i-L´ _j|⩽1 for every pair of processors i and j . Several heuristics for load balancing, both on a hypercube and on other parallel computers, have been proposed. None of these takes into account the time needed to actually redistribute the load. This time could be significant if load redistribution involves the transmission of long files. The present paper is concerned with load balancing on a hypercube under the assumption that moving k units of load from one processor to a neighbor processor takes k units of time. It is interested in balancing load as well as minimizing the load transfer time. As an example it considers a four processor hypercube