On Finding Small 2-Generating Sets

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 + ε for any ε > 0. We then prove our main result, which consists in a representation lemma for minimum cardinality 2-generating sets.

• Type: Conference
• Year: 2009
• Where: COCOON
• Authors: Isabelle Fagnot, Guillaume Fertin, Stéphane Vialette
• Keywords: 2-generating Sets, COCOON 2009, Combinatorics, Minimum Cardinality, Minimum Cardinality Set