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

• URL: http://arxiv.org/abs/2202.05938v1
• Date: Fri, 11 Feb 2022 23:53:43 GMT
• Title: Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits
• Authors: Pierre Bourhis (1), Laurence Duchien (1), J\'er\'emie Dusart (1), Emmanuel Lonca (2), Pierre Marquis (2 and 3), Cl\'ement Quinton (1) ((1) University of Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, (2) Univ. Artois, CNRS, UMR 8188 CRIL, (3) Institut Universitaire de France)
• Abstract summary: We present an algorithm that computes $k$ models of $C$ among those having the largest values w.r. $$. We also present a pseudo-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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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