k-partitioning problems for maximizing the minimum load

The optimization versions of the k-PARTITIONING problems are considered in this paper. For the objective to maximize the minimum load of m subsets, we first show that the FOLDING algorithm has a tight worst case ratio of max{2/k, 1/m}. Then, we present an algorithm called HARMONIC1 with a worst case ratio at least max{l/k, 1/([Sigma(i=1)(m) 1/i] + 1)}. It concludes the HARMONIC1 is better than FOLDING for k > 2([Sigma(i=1)(m) 1/i] + 1). We further show that HARMONIC1 is asymptotically optimal ordinal algorithm. We also present an algorithm HARMONIC2 for solving the general k(i)-PARTITIONING problem. (C) 2003 Elsevier Ltd. All rights reserved.