  The research in parallel machine scheduling in combinatorial optimization
suggests that the desirable parallel efficiency could be achieved when the jobs
are sorted in the non-increasing order of processing times. In this paper, we
find that the time spending for computing the permanent of a sparse matrix by
hybrid algorithm is strongly correlated to its permanent value. A strategy is
introduced to improve a parallel algorithm for sparse permanent. Methods for
approximating permanents, which have been studied extensively, are used to
approximate the permanent values of sub-matrices to decide the processing order
of jobs. This gives an improved load balancing method. Numerical results show
that the parallel efficiency is improved remarkably for the permanents of
fullerene graphs, which are of great interests in nanoscience.
