Efficient Enumeration of Solutions Produced by Closure Operations

Arnaud Mary (1, 2) , Yann Strozecki (3)

1 ERABLE - Equipe de recherche européenne en algorithmique et biologie formelle et expérimentale
2 Baobab
3 DAVID - Données et algorithmes pour une ville intelligente et durable - DAVID

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of "set operations" (e.g. by union, intersection, difference, symmetric difference ...). To do so, we prove that for any set of operations F, one can decide in polynomial time whether an element belongs to the closure by F of a family of sets. When the relation is over a domain larger than two elements, we prove that our generic enumeration method fails, since the associated decision problem is NP-hard.

Mots clés: enumeration; set saturation; polynomial delay; Post’s lattice

Domaines: Algorithme et structure de données [cs.DS]

Arnaud Mary, Yann Strozecki. Efficient Enumeration of Solutions Produced by Closure Operations. 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016, Feb 2016, Orléans, France. ⟨10.4230/LIPIcs.STACS.2016.52⟩. ⟨hal-01388505⟩