54 research outputs found
A BTP-Based Family of Variable Elimination Rules for Binary CSPs
International audienceThe study of broken-triangles is becoming increasingly ambitious , by both solving constraint satisfaction problems (CSPs) in polynomial time and reducing search space size through value merging or variable elimination. Considerable progress has been made in extending this important concept, such as dual broken-triangle and weakly broken-triangle, in order to maximize the number of captured tractable CSP instances and/or the number of merged values. Specifically, m-wBTP allows to merge more values than BTP. k-BTP, WBTP and m-BTP permit to capture more tractable instances than BTP. Here, we introduce a new weaker form of BTP, which will be called m-fBTP for flexible broken-triangle property. m-fBTP allows on the one hand to eliminate more variables than BTP while preserving satisfiability and on the other to define new bigger tractable class for which arc consistency is a decision procedure. Likewise, m-fBTP permits to merge more values than BTP but less than m-wBTP
On Broken Triangles (IJCAI 2016)
International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP
On Broken Triangles
A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP
Hybrid Tractable Classes of Binary Quantified Constraint Satisfaction Problems
In this paper, we investigate the hybrid tractability of binary Quantified
Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of
binary QCSPs is identified by using the broken-triangle property. In this
class, the variable ordering for the broken-triangle property must be same as
that in the prefix of the QCSP. Second, we break this restriction to allow that
existentially quantified variables can be shifted within or out of their
blocks, and thus identify some novel tractable classes by introducing the
broken-angle property. Finally, we identify a more generalized tractable class,
i.e., the min-of-max extendable class for QCSPs
Autour des Triangles Cassés
National audienceUne instance CSP binaire qui satisfait la propriété des triangles cassés (BTP) peut etre résolue en temps polynomial. Malheureusement, en pratique, peu d'ins-tances satisfont cette propriété. Nous montrons qu'une version locale de BTP permet de fusionner des valeurs dans les domaines d'instances binaires quelconques. Des expérimentations démontrent la diminution significative de la taille de l'instance pour certaines classes de pro-bì emes. Ensuite, nous proposons une généralisation de cette fusion a des contraintes d'arité quelconque. En-fin, une version orientée nous permet d'´ etendre la classe polynomiale BTP. Ce papier est un résumé de l'article M. C. Cooper, A. El Mouelhi, C. Terrioux et B. Zanuttini. On Broken Triangles In Proceedings of CP,LNCS 8656, 9–24, 2014
Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems
International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in arbitrary instances of binary CSP, thus providing a novel polynomial-time reduction operation. Extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity and we investigate the theoretical relationship with resolution in SAT. A directional version of general-arity BTP-merging then allows us to extend the BTP tractable class previously defined only for binary CSP. We investigate the complexity of several related problems including the recognition problem for the general-arity BTP class when the variable order is unknown, finding an optimal order in which to apply BTP merges and detecting BTP-merges in the presence of global constraints such as AllDifferent
Hybrid tractability of soft constraint problems
The constraint satisfaction problem (CSP) is a central generic problem in
computer science and artificial intelligence: it provides a common framework
for many theoretical problems as well as for many real-life applications. Soft
constraint problems are a generalisation of the CSP which allow the user to
model optimisation problems. Considerable effort has been made in identifying
properties which ensure tractability in such problems. In this work, we
initiate the study of hybrid tractability of soft constraint problems; that is,
properties which guarantee tractability of the given soft constraint problem,
but which do not depend only on the underlying structure of the instance (such
as being tree-structured) or only on the types of soft constraints in the
instance (such as submodularity). We present several novel hybrid classes of
soft constraint problems, which include a machine scheduling problem,
constraint problems of arbitrary arities with no overlapping nogoods, and the
SoftAllDiff constraint with arbitrary unary soft constraints. An important tool
in our investigation will be the notion of forbidden substructures.Comment: A full version of a CP'10 paper, 26 page
Variable and value elimination in binary constraint satisfaction via forbidden patterns
Variable or value elimination in a constraint satisfaction problem (CSP) can
be used in preprocessing or during search to reduce search space size. A
variable elimination rule (value elimination rule) allows the polynomial-time
identification of certain variables (domain elements) whose elimination,
without the introduction of extra compensatory constraints, does not affect the
satisfiability of an instance. We show that there are essentially just four
variable elimination rules and three value elimination rules defined by
forbidding generic sub-instances, known as irreducible existential patterns, in
arc-consistent CSP instances. One of the variable elimination rules is the
already-known Broken Triangle Property, whereas the other three are novel. The
three value elimination rules can all be seen as strict generalisations of
neighbourhood substitution.Comment: A full version of an IJCAI'13 paper to appear in Journal of Computer
and System Sciences (JCSS
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