Enumerating models of DNF faster: breaking the dependency on the formula size

Énumérer les modèles des DNF plus rapidement : enlever la dépendance en la taille de la formule

Florent Capelli (1) , Yann Strozecki (2)

1 LINKS - Linking Dynamic Data
2 DAVID - Données et algorithmes pour une ville intelligente et durable - DAVID

In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula. We succeed for two subclasses of DNF formulas: we provide a constant delay algorithm for k-DNF with fixed k by an appropriate amortization method and we give a polynomial delay algorithm for monotone formulas. We then focus on the average delay of enumeration algorithms and show that we can bring down the dependency of the average delay to the square root of the formula size and even to a logarithmic dependency for monotone formulas.

Mots clés: Computational complexity; Enumeration; DNF

Domaines: Complexité [cs.CC]

Florent Capelli, Yann Strozecki. Enumerating models of DNF faster: breaking the dependency on the formula size. Discrete Applied Mathematics, 2020, ⟨10.1016/j.dam.2020.02.014⟩. ⟨hal-01891483⟩