Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits

Bourhis, Pierre; Duchien, Laurence; Dusart, Jérémie; Lonca, Emmanuel; Marquis, Pierre; Quinton, Clément

Type de document :

Pré-publication ou Document de travail

Titre :

Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits

Auteur(s) :

Bourhis, Pierre [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Self-adaptation for distributed services and large software systems [SPIRALS]
Duchien, Laurence [Auteur]
Self-adaptation for distributed services and large software systems [SPIRALS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Dusart, Jérémie [Auteur]
Self-adaptation for distributed services and large software systems [SPIRALS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Lonca, Emmanuel [Auteur]
Centre de Recherche en Informatique de Lens [CRIL]
Marquis, Pierre [Auteur]
Centre de Recherche en Informatique de Lens [CRIL]
Quinton, Clément [Auteur]

Self-adaptation for distributed services and large software systems [SPIRALS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Discipline(s) HAL :

Informatique [cs]

Résumé en anglais : [en]

We are interested in computing $k$ most preferred models of a given d-DNNF circuit $C$, where the preference relation is based on an algebraic structure called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In ...
Lire la suite >We are interested in computing $k$ most preferred models of a given d-DNNF circuit $C$, where the preference relation is based on an algebraic structure called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In our setting, every literal in $C$ has a value in $K$ and the value of an assignment is an element of $K$ obtained by aggregating using $\otimes$ the values of the corresponding literals. We present an algorithm that computes $k$ models of $C$ among those having the largest values w.r.t. $<$, and show that this algorithm runs in time polynomial in $k$ and in the size of $C$. We also present a pseudo polynomial-time algorithm for deriving the top-$k$ values that can be reached, provided that an additional (but not very demanding) requirement on the semigroup is satisfied. Under the same assumption, we present a pseudo polynomial-time algorithm that transforms $C$ into a d-DNNF circuit $C'$ satisfied exactly by the models of $C$ having a value among the top-$k$ ones. Finally, focusing on the semigroup $(\mathbb{N}, +, <)$, we compare on a large number of instances the performances of our compilation-based algorithm for computing $k$ top solutions with those of an algorithm tackling the same problem, but based on a partial weighted MaxSAT solver.Lire moins >

Langue :

Anglais

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

Fichiers

http://arxiv.org/pdf/2202.05938
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2202.05938
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