On uniform k-partition problems

Authors:
Paolo Dell'Olmo;Pierre Hansen;Stefano Pallottino;Giovanni Storchi
Affiliations:
Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma "La Sapienza", Roma, Italy;GERAD and École des Hautes Etudes Commerciales, Chemin de la Côte-Sainte-Catherine Montréal, Qué., Canada;Dipartimento di Informatica, Università di Pisa, Pisa, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma "La Sapienza", Roma, Italy
Venue:
Discrete Applied Mathematics - Special issue: Max-algebra
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.