On Finding Small 2-Generating Sets

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 + epsilon for any epsilon > 0. We then prove our main result, which consists in a representation lemma for minimum cardinality 2-generating sets.
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Isabelle Fagnot, Guillaume Fertin, Stéphane Vialette. On Finding Small 2-Generating Sets. COCOON 2009, 2009, Niagara Falls, United States. pp.378-387, ⟨10.1007/978-3-642-02882-3_38⟩. ⟨hal-00416577⟩

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