k-Partitioning problems with partition matroid constraint

In this paper, we consider the k-partitioning problems with partition matroid constraint and present an algorithm called the layered LPT algorithm. With the objective of minimizing the maximum load, we show that the layered LPT algorithm has a tight worst case ratio of 2−1/m. With the objective of maximizing the minimum load, we show that the layered LPT algorithm has a tight worst case ratio of 1/m for the general case and, with certain conditions, the worst ratio can be improved to m/(2m−1) for the general k case and to (m−1)/(2m−3) for the k=3 case.