51 research outputs found
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
Translation-based Constraint Answer Set Solving
We solve constraint satisfaction problems through translation to answer set
programming (ASP). Our reformulations have the property that unit-propagation
in the ASP solver achieves well defined local consistency properties like arc,
bound and range consistency. Experiments demonstrate the computational value of
this approach.Comment: Self-archived version for IJCAI'11 Best Paper Track submissio
Proteus: A Hierarchical Portfolio of Solvers and Transformations
In recent years, portfolio approaches to solving SAT problems and CSPs have
become increasingly common. There are also a number of different encodings for
representing CSPs as SAT instances. In this paper, we leverage advances in both
SAT and CSP solving to present a novel hierarchical portfolio-based approach to
CSP solving, which we call Proteus, that does not rely purely on CSP solvers.
Instead, it may decide that it is best to encode a CSP problem instance into
SAT, selecting an appropriate encoding and a corresponding SAT solver. Our
experimental evaluation used an instance of Proteus that involved four CSP
solvers, three SAT encodings, and six SAT solvers, evaluated on the most
challenging problem instances from the CSP solver competitions, involving
global and intensional constraints. We show that significant performance
improvements can be achieved by Proteus obtained by exploiting alternative
view-points and solvers for combinatorial problem-solving.Comment: 11th International Conference on Integration of AI and OR Techniques
in Constraint Programming for Combinatorial Optimization Problems. The final
publication is available at link.springer.co
- …