On uniform k-partition problems

Authors:
Paolo Dell'Olmo;Pierre Hansen;Stefano Pallottino;Giovanni Storchi
Affiliations:
Dipartimento di Statistica, Probabilití e Statistiche Applicate, Universití di Roma"La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy;GERAD and ícole des Hautes Etudes Commerciales, 3000, Chemin de la Côte-Sainte-Catherine Montréal, Qué., Canada H3T 2A7;Dipartimento di Informatica, Universití di Pisa, Via F. Buonarroti 2, 56127 Pisa, Italy;Dipartimento di Statistica, Probabilití e Statistiche Applicate, Universití di Roma "La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

We study various uniform k-partition problems which consist in partitioning m sets, each of cardinality k, into k sets of cardinality m such that each of these sets contains exactly one element from every original set. The problems differ according to the particular measure of ''set uniformity'' to be optimized. Most problems are polynomial and 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.