The Power of Local Consistency in Conjunctive Queries and Constraint Satisfaction Problems

2017 ◽  
Vol 46 (3) ◽  
pp. 1111-1145 ◽  
Author(s):  
Gianluigi Greco ◽  
Francesco Scarcello
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Local Consistency ◽  
Conjunctive Queries

scholarly journals Constraint programming viewed as rule-based programming

2001 ◽  
Vol 1 (6) ◽  
pp. 713-750 ◽  
Author(s):  
KRZYSZTOF R. APT ◽  
ERIC MONFROY
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Rule Based ◽  
Local Consistency ◽  
Arc Consistency ◽  
Computation Process ◽  
Rule Based Approach ◽  
Rule Consistency

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

Efficient Singleton Consistency by Combining Forward Checking and Bound Consistency

2014 ◽  
Vol 23 (04) ◽  
pp. 1460017
Author(s):  
Jinsong Guo ◽  
Hongbo Li ◽  
Zhanshan Li ◽  
Yonggang Zhang ◽  
Xianghua Jia
Keyword(s):  
Constraint Satisfaction ◽  
Search Algorithm ◽  
Computational Cost ◽  
Search Space ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Local Consistency ◽  
Arc Consistency ◽  
Strong Bound

Maintaining local consistencies can improve the efficiencies of the search algorithms solving constraint satisfaction problems (CSPs). Comparing with arc consistency which is the most widely used local consistency, stronger local consistencies can make the search space smaller while they require higher computational cost. In this paper, we make an attempt on the compromise between the pruning ability and the computational cost. A new local consistency called singleton strong bound consistency (SSBC) and its light version, light SSBC, are proposed. The search algorithm maintaining light SSBC can outperform MAC on a considerable number of problems.

scholarly journals Using Pivot Consistency to Decompose and Solve Functional CSPs

1995 ◽  
Vol 2 ◽  
pp. 447-474 ◽  
Author(s):  
P. David
Keyword(s):  
Structural Properties ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
New Method ◽  
Functional Constraints ◽  
Local Consistency ◽  
Semantic Properties

Many studies have been carried out in order to increase thesearch efficiency of constraint satisfaction problems; among them,some make use of structural properties of the constraintnetwork; others take into account semantic properties of theconstraints, generally assuming that all the constraints possessthe given property. In this paper, we propose a new decompositionmethod benefiting from both semantic properties of functional constraints (not bijective constraints) and structuralproperties of the network; furthermore, not all the constraints needto be functional. We show that under some conditions, the existenceof solutions can be guaranteed. We first characterize a particularsubset of the variables, which we name a root set. We thenintroduce pivot consistency, a new local consistency which is aweak form of path consistency and can be achieved in O(n^2d^2)complexity (instead of O(n^3d^3) for path consistency), and wepresent associated properties; in particular, we show that anyconsistent instantiation of the root set can be linearly extended to a solution, which leads to the presentation of the aforementioned new method for solving by decomposing functional CSPs.

scholarly journals Local Consistency and SAT-Solvers

2012 ◽  
Vol 43 ◽  
pp. 329-351 ◽  
Author(s):  
P. Jeavons ◽  
J. Petke
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Inference Rule ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Fixed Size ◽  
Local Consistency ◽  
Sat Solvers ◽  
Clause Learning ◽  
Do So

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem is precisely captured by using a particular inference rule, which we call negative-hyper-resolution, on the standard direct encoding of the problem into Boolean clauses. We also show that current clause-learning SAT-solvers will discover in expected polynomial time any inconsistency that can be deduced from a given set of clauses using negative-hyper-resolvents of a fixed size. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all fixed values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of constraint problems which are challenging for conventional constraint-programming solvers.

HyperBench

2021 ◽  
Vol 26 ◽  
pp. 1-40
Author(s):  
Wolfgang Fischl ◽  
Georg Gottlob ◽  
Davide Mario Longo ◽  
Reinhard Pichler
Keyword(s):  
Constraint Satisfaction ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Large Set ◽  
Web Interface ◽  
Conjunctive Queries ◽  
Practical Algorithms ◽  
New Infrastructure

To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed—giving rise to different notions of width, noticeably, plain, generalized, and fractional hypertree width (hw, ghw, and fhw). Given the increasing interest in using such decomposition methods in practice, a publicly accessible repository of decomposition software, as well as a large set of benchmarks, and a web-accessible workbench for inserting, analyzing, and retrieving hypergraphs are called for. We address this need by providing (i) concrete implementations of hypergraph decompositions (including new practical algorithms), (ii) a new, comprehensive benchmark of hypergraphs stemming from disparate CQ and CSP collections, and (iii) HyperBench, our new web-interface for accessing the benchmark and the results of our analyses. In addition, we describe a number of actual experiments we carried out with this new infrastructure.

scholarly journals Complexity Analysis of Generalized and Fractional Hypertree Decompositions

2021 ◽  
Vol 68 (5) ◽  
pp. 1-50
Author(s):  
Georg Gottlob ◽  
Matthias Lanzinger ◽  
Reinhard Pichler ◽  
Igor Razgon
Keyword(s):  
Polynomial Time ◽  
Constraint Satisfaction ◽  
Open Problem ◽  
Complexity Analysis ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Conjunctive Queries ◽  
Np Completeness ◽  
Np Complete ◽  
Efficient Approximation

Hypertree decompositions (HDs), as well as the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHDs) are hypergraph decomposition methods successfully used for answering conjunctive queries and for solving constraint satisfaction problems. Every hypergraph H has a width relative to each of these methods: its hypertree width hw(H) , its generalized hypertree width ghw(H) , and its fractional hypertree width fhw(H) , respectively. It is known that hw(H)≤ k can be checked in polynomial time for fixed k , while checking ghw(H)≤ k is NP-complete for k ≥ 3 . The complexity of checking fhw(H)≤ k for a fixed k has been open for over a decade. We settle this open problem by showing that checking fhw(H)≤ k is NP-complete, even for k=2 . The same construction allows us to prove also the NP-completeness of checking ghw(H)≤ k for k=2 . After that, we identify meaningful restrictions that make checking for bounded ghw or fhw tractable or allow for an efficient approximation of the fhw .

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