Revising Hull and Box Consistency

@inproceedings{Benhamou1999RevisingHA,
  title={Revising Hull and Box Consistency},
  author={Fr{\'e}d{\'e}ric Benhamou and Fr{\'e}d{\'e}ric Goualard and Laurent Granvilliers and Jean-François Puget},
  booktitle={ICLP},
  year={1999}
}
Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper first presents HC4, an algorithm to enforce hull consistency without decomposing complex constraints into primitives. Next, an extended definition for box consistency is given and the resulting consistency is shown to subsume hull consistency. Finally… Expand
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References

SHOWING 1-10 OF 18 REFERENCES
Interval Constraint Logic Programming
  • F. Benhamou
  • Mathematics, Computer Science
  • Constraint Programming
  • 1994
TLDR
An overview on the use of interval arithmetic to process numerical constraints in Constraint Logic Programming, and the description of the general framework based on approximations, on its application to interval constraint solving over continuous and discrete quantities is presented. Expand
CLP(Intervals) Revisited
TLDR
Experimental results indicate that Newton outperforms existing languages by an order of magnitude and is competitive with some state-of-the-art tools on some standard benchmarks. Expand
An Extension of the WAM for Hybrid Interval Solvers
TLDR
The extension of the WAM instruction set necessary to support the new features of DecLIC is described, along with the new internal structures, and benchmark comparisons show that combination permits, on certain cases, relevant speed-ups in the resolution process. Expand
Numerica: A Modeling Language for Global Optimization
TLDR
The meaning and implementation of Numerica: overview of the algorithm domain-specific and monotonic interval extensions constraint solving unconstrained optimization constrained optimization advanced techniques an implementation of box consistency. Expand
A C++ implementation of CLP
TLDR
A C++ library that embodies Constraint Logic Programming (CLP) concepts such as logical variables, incremental constraint satisfaction and backtracking, and which combines Object Oriented Programming (OOP) with CLP. Expand
Applying Interval Arithmetic to Real, Integer, and Boolean Constraints
TLDR
A unified processing for real, integer, and Boolean constraints based on a general narrowing algorithm which applies to any n-ary relation on R is presented and a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals, and Reals is proposed. Expand
Consistency in Networks of Relations
TLDR
The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency algorithm, to discuss their relationships and the may applications, both realized and potential of network consistency algorithms. Expand
Comparing Partial Consistencies
TLDR
The relations among the different partial consistencies which are main emphasis of these algorithms are stated and the capability of these partial consistency to handle the so-called dependency problem is analysed. Expand
Constraint Arithmetic on Real Intervals
TLDR
Constraint interval arithmetic is a sublanguage of BNR Prolog which takes a new approach to the old problem of deriving numerical consequences from algebraic models by bypassing the traditional dichotomy between (numeric) calculation and (symbolic) proofs. Expand
On automatic differentiation
TLDR
Simulation of the radionucleide transport in underground in order to determine the impact of a possible propagation of radioelements and the modelling of the flow in porous media around the storage requires to know the physical parameters of the different geological layers. Expand
...
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