Parallel Approximation Algorithms for Bin Packing

We study the parallel complexity of polynomial heuristics for the bin packing problem. We show that some well-known (and simple) methods like first-fit-decreasing are P-complete, and it is hence very unlikely that they can be efficiently parallelized. On the other hand, we exhibit an optimal NC algorithm that achieves the same performance bound as does FFD. Finally, we discuss parallelization of polynomial approximation algorithms for bin packing based on discretization. OThe first two authors were supported in part by a grant from the AT&T Foundation, ONR contract N00014-85-C-0731, and NSF grant DCR-8351757; the third author acknowledges the support of ONR grant N00014-86-K-0454.