scholarly journals Set Intersection and Consistency in Constraint Networks

2006 ◽  
Vol 27 ◽  
pp. 441-464 ◽  
Author(s):  
Y. Zhang ◽  
R. H. C. Yap
Keyword(s):  
Close Relation ◽  
Convex Constraints ◽  
Local Consistency ◽  
Constraint Networks ◽  
New Class ◽  
Constraint Network ◽  
Consistency Results ◽  
Set Intersection ◽  
Global Consistency ◽  
Consistency Properties

In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This approach not only simplifies the understanding of and unifies many existing consistency results, but also directs the study of consistency to that of set intersection properties in many situations, as demonstrated by the results on the convexity and tightness of constraints in this paper. Specifically, we identify a new class of tree convex constraints where local consistency ensures global consistency. This generalizes row convex constraints. Various consistency results are also obtained on constraint networks where only some, in contrast to all in the existing work,constraints are tight.

Leveraging Variable Elimination for Efficiently Reasoning about Qualitative Constraints

2018 ◽  
Vol 27 (04) ◽  
pp. 1860001 ◽  
Author(s):  
Michael Sioutis ◽  
Zhiguo Long ◽  
Sanjiang Li
Keyword(s):  
Graphical Models ◽  
State Of The Art ◽  
Exact Inference ◽  
Local Consistency ◽  
Constraint Networks ◽  
Constraint Network ◽  
Variable Elimination ◽  
Region Connection Calculus ◽  
Effective Manner ◽  
Novel Algorithm

We introduce, study, and evaluate a novel algorithm in the context of qualitative constraint-based spatial and temporal reasoning that is based on the idea of variable elimination, a simple and general exact inference approach in probabilistic graphical models. Given a qualitative constraint network [Formula: see text], our algorithm utilizes a particular directional local consistency, which we denote by [Formula: see text]-consistency, in order to efficiently decide the satisfiability of [Formula: see text]. Our discussion is restricted to distributive subclasses of relations, i.e., sets of relations closed under converse, intersection, and weak composition and for which weak composition distributes over non-empty intersections for all of their relations. We demonstrate that enforcing [Formula: see text]-consistency in a given qualitative constraint network defined over a distributive subclass of relations allows us to decide its satisfiability, and obtain similar useful results for the problems of minimal labelling and redundancy. Further, we present a generic method that allows extracting a scenario from a satisfiable network, i.e., an atomic satisfiable subnetwork of that network, in a very simple and effective manner. The experimentation that we have conducted with random and real-world qualitative constraint networks defined over a distributive subclass of relations of the Region Connection Calculus and the Interval Algebra, shows that our approach exhibits unparalleled performance against state-of-the-art approaches for checking the satisfiability of such constraint networks.

scholarly journals Strategyproof and Fair Matching Mechanism for Union of Symmetric M-convex Constraints

2018 ◽  
Author(s):  
Yuzhe Zhang ◽  
Kentaro Yahiro ◽  
Nathanaël Barrot ◽  
Makoto Yokoo
Keyword(s):  
Convex Sets ◽  
Real Life ◽  
Convex Constraints ◽  
New Class ◽  
Distributional Constraints ◽  
Deferred Acceptance ◽  
Matching Mechanism

In this paper, we identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a variety of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints in general. Thus, developing a fair and strategyproof mechanism that can handle this class is challenging. We present a novel mechanism called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard DA mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets. Furthermore, in comparison to a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA), QRDA always obtains a weakly better matching for students and, experimentally, performs better in terms of nonwastefulness.

An LMS-Based Grammar Self-index with Local Consistency Properties

2021 ◽  
pp. 100-113
Author(s):  
Diego Díaz-Domínguez ◽  
Gonzalo Navarro ◽  
Alejandro Pacheco
Keyword(s):  
Local Consistency ◽  
Consistency Properties

scholarly journals Domain Filtering Consistencies

2001 ◽  
Vol 14 ◽  
pp. 205-230 ◽  
Author(s):  
R. Debruyne ◽  
C. Bessiere
Keyword(s):  
Search Algorithms ◽  
Basic Question ◽  
Large Networks ◽  
Local Consistency ◽  
Constraint Network ◽  
Arc Consistency ◽  
Constraint Graph ◽  
Constraint Reasoning ◽  
Time Required

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.

scholarly journals A Simple Cocyclic Jacket Matrices

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Moon Ho Lee ◽  
Gui-Liang Feng ◽  
Zhu Chen
Keyword(s):  
Finite Field ◽  
Number Field ◽  
Complex Number ◽  
Close Relation ◽  
Theoretical Physics ◽  
Unitary Matrices ◽  
New Class ◽  
Hand Tool ◽  
The Common ◽  
Complex Number Field

We present a new class of cocyclic Jacket matrices over complex number field with any size. We also construct cocyclic Jacket matrices over the finite field. Such kind of matrices has close relation with unitary matrices which are a first hand tool in solving many problems in mathematical and theoretical physics. Based on the analysis of the relation between cocyclic Jacket matrices and unitary matrices, the common method for factorizing these two kinds of matrices is presented.

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