Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits   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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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn