26,292 research outputs found
Beyond Hypertree Width: Decomposition Methods Without Decompositions
The general intractability of the constraint satisfaction problem has
motivated the study of restrictions on this problem that permit polynomial-time
solvability. One major line of work has focused on structural restrictions,
which arise from restricting the interaction among constraint scopes. In this
paper, we engage in a mathematical investigation of generalized hypertree
width, a structural measure that has up to recently eluded study. We obtain a
number of computational results, including a simple proof of the tractability
of CSP instances having bounded generalized hypertree width
Generalized Majority-Minority Operations are Tractable
Generalized majority-minority (GMM) operations are introduced as a common
generalization of near unanimity operations and Mal'tsev operations on finite
sets. We show that every instance of the constraint satisfaction problem (CSP),
where all constraint relations are invariant under a (fixed) GMM operation, is
solvable in polynomial time. This constitutes one of the largest tractable
cases of the CSP
The complexity of quantified constraints using the algebraic formulation
Peer reviewedFinal Published versio
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
Message passing for quantified Boolean formulas
We introduce two types of message passing algorithms for quantified Boolean
formulas (QBF). The first type is a message passing based heuristics that can
prove unsatisfiability of the QBF by assigning the universal variables in such
a way that the remaining formula is unsatisfiable. In the second type, we use
message passing to guide branching heuristics of a Davis-Putnam
Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on
random QBFs our branching heuristics gives robust exponential efficiency gain
with respect to the state-of-art solvers. We also manage to solve some
previously unsolved benchmarks from the QBFLIB library. Apart from this our
study sheds light on using message passing in small systems and as subroutines
in complete solvers.Comment: 14 pages, 7 figure
QCSP on partially reflexive forests
We study the (non-uniform) quantified constraint satisfaction problem QCSP(H)
as H ranges over partially reflexive forests. We obtain a complexity-theoretic
dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is
related firstly to connectivity, and thereafter to accessibility from all
vertices of H to connected reflexive subgraphs. In the case of partially
reflexive paths, we give a refinement of our dichotomy: QCSP(H) is either in NL
or is Pspace-complete
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