111 research outputs found
Comparison of PBO solvers in a dependency solving domain
Linux package managers have to deal with dependencies and conflicts of
packages required to be installed by the user. As an NP-complete problem, this
is a hard task to solve. In this context, several approaches have been pursued.
Apt-pbo is a package manager based on the apt project that encodes the
dependency solving problem as a pseudo-Boolean optimization (PBO) problem. This
paper compares different PBO solvers and their effectiveness on solving the
dependency solving problem.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
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