One-Dimensional Partitioning for Heterogeneous Systems: Theory and Practice

We study the problem of one-dimensional partitioning of nonuniform workload arrays with optimal load balancing for heterogeneous systems. We look at two cases: chain-on-chain partitioning, where the order of the processors is specified, and chain partitioning, where processor permutation is allowed. We present polynomial time algorithms to solve the chain-on-chain partitioning problem optimally, while we prove that the chain partition is NP-complete. Our empirical studies show that our proposed exact algorithms produce substantially better results than heuristics while the solution times remain comparable