On uniform k-partition problems

In this work we study various uniform $k$-partition problems which consist in partitioning a collection of $m$ sets, each of them of cardinality $k$, into $k$ sets of cardinality $m$ such that each of these sets contains exactly one element coming from every original set. The problems differ according to the particular measure of ``set uniformity'' to be optimized. Most of the studied problems are polynomial and the corresponding solution algorithms are provided. A few of them are proved to be NP-hard. Examples of applications to scheduling and routing problems are also discussed