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 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.

Constraint Satisfaction Problems Solvable by Local Consistency Methods

2014 ◽  
Vol 61 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Libor Barto ◽  
Marcin Kozik
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Local Consistency

scholarly journals Fast and Parallel Decomposition of Constraint Satisfaction Problems

2020 ◽  
Author(s):  
Georg Gottlob ◽  
Cem Okulmus ◽  
Reinhard Pichler
Keyword(s):  
Structural Properties ◽  
Constraint Satisfaction ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Query Answering ◽  
Conjunctive Query ◽  
Minimal Width ◽  
Parallel Decomposition

Constraint Satisfaction Problems (CSP) are notoriously hard. Consequently, powerful decomposition methods have been developed to overcome this complexity. However, this poses the challenge of actually computing such a decomposition for a given CSP instance, and previous algorithms have shown their limitations in doing so. In this paper, we present a number of key algorithmic improvements and parallelisation techniques to compute so-called Generalized Hypertree Decompositions (GHDs) faster. We thus advance the ability to compute optimal (i.e., minimal-width) GHDs for a significantly wider range of CSP instances on modern machines. This lays the foundation for more systems and applications in evaluating CSPs and related problems (such as Conjunctive Query answering) based on their structural properties.

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.

SUCCESSIVE SEARCH METHOD FOR SOLVING VALUED CONSTRAINT SATISFACTION AND OPTIMIZATION PROBLEMS

2002 ◽  
Vol 11 (03) ◽  
pp. 425-436 ◽  
Author(s):  
MOHAMED TOUNSI ◽  
PHILIPPE DAVID
Keyword(s):  
Lower Bound ◽  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Main Idea ◽  
Earth Observation ◽  
Constraint Satisfaction Problems ◽  
Search Method ◽  
New Method ◽  
Earth Observation Satellite ◽  
Russian Doll Search

In this paper we introduce a new method based on Russian Doll Search (RDS) for solving optimization problems expressed as Valued Constraint Satisfaction Problems (VCSPs). The RDS method solves problems of size n (where n is the number of variables) by replacing one search by n successive searches on nested subproblems using the results of each search to produce a better lower bound. The main idea of our method is to introduce the variables through the successive searches not one by one but by sets of k variables. We present two variants of our method: the first one where the number k is fixed, noted kfRDS; the second one, kvRDS, where k can be variable. Finally, we show that our method improves RDS on daily management of an earth observation satellite.

scholarly journals Generating Hard Satisfiable Formulas by Hiding Solutions Deceptively

2007 ◽  
Vol 28 ◽  
pp. 107-118 ◽  
Author(s):  
H. Jia ◽  
C. Moore ◽  
D. Strain
Keyword(s):  
Polynomial Time ◽  
Constraint Satisfaction ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Experimental Results ◽  
New Method ◽  
Truth Assignment ◽  
Benchmark Instances ◽  
Problem Generator

To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose clauses randomly from among those satisfied by A. However, this method tends to produce easy problems, since the majority of literals point toward the "hidden'' assignment A. Last year, Achlioptas, Jia and Moore proposed a problem generator that cancels this effect by hiding both A and its complement. While the resulting formulas appear to be just as hard for DPLL algorithms as random 3-SAT formulas with no hidden assignment, they can be solved by WalkSAT in only polynomial time. Here we propose a new method to cancel the attraction to A, by choosing a clause with t > 0 literals satisfied by A with probability proportional to q^t for some q < 1. By varying q, we can generate formulas whose variables have no bias, i.e., which are equally likely to be true or false; we can even cause the formula to "deceptively'' point away from A. We present theoretical and experimental results suggesting that these formulas are exponentially hard both for DPLL algorithms and for incomplete algorithms such as WalkSAT.

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.

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
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