On Finding Small 2-Generating Sets

Authors:
Isabelle Fagnot;Guillaume Fertin;Stéphane Vialette
Affiliations:
IGM-LabInfo, CNRS UMR 8049, Université Paris-Est, 5 Bd Descartes 77454 Marne-la-Vallée, France, and Université Paris Diderot, Paris 7, France;Laboratoire d'Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241, Université de Nantes, Nantes Cedex 3, France 44322;IGM-LabInfo, CNRS UMR 8049, Université Paris-Est, Marne-la-Vallée, France 77454
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

Given a set of positive integers S , we consider the problem of finding a minimum cardinality set of positive integers X (called a minimum 2-generating set of S ) s.t. every element of S is an element of X or is the sum of two (non-necessarily distinct) elements of X . We give elementary properties of 2-generating sets and prove that finding a minimum cardinality 2-generating set is hard to approximate within ratio 1 + *** for any *** 0. We then prove our main result, which consists in a representation lemma for minimum cardinality 2-generating sets.