Global consistency for continuous constraints

Haroud, Djamila; Faltings, Boi

doi:10.1007/3-540-58601-6_88

Cited by 12 publications

(10 citation statements)

References 10 publications

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“…By splitting the initial box and evaluating the corresponding Bernstein coefficients, one can isolate all the boxes verifying a set of inequality constraints. Haroud and Faltings [1994] did not rely on Algorithm Subpaving. Instead, they represented explicitly the subpaving of the relation ρ c associated to each n-ary inequality constraint by a 2 n -tree of boxes.…”

Section: Related Workmentioning

confidence: 99%

Interval constraint solving for camera control and motion planning

Benhamou

Goualard

Languénou

et al. 2004

ACM Trans. Comput. Logic

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Many problems in robust control and motion planning can be reduced to either finding a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the "guaranteed tuning problem" as defined by Jaulin and Walter, which amounts to finding a value for some tuning parameter such that a set of inequalities be verified for all the possible values of some perturbation vector. A classical approach to solving these problems, which satisfies the strong soundness requirement, involves some quantifier elimination procedure such as Collins' Cylindrical Algebraic Decomposition symbolic method. Sound numerical methods using interval arithmetic and local consistency enforcement to prune the search space are presented in this article as much faster alternatives for both soundly solving systems of nonlinear inequalities, and addressing the guaranteed tuning problem whenever the perturbation vector has dimension 1. The use of these methods in camera control is investigated, and experiments with the prototype of a declarative modeler to express camera motion using a cinematic language are reported and commented upon.

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Section: Related Workmentioning

confidence: 99%

Interval constraint solving for camera control and motion planning

Benhamou

Goualard

Languénou

et al. 2004

ACM Trans. Comput. Logic

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“…A purely closed form approach, as adopted by constraint programming systems [8,15] has several drawbacks. First, closed form solutions are not always feasible for arbitrary queries.…”

Section: Query Semantics and Griddingmentioning

confidence: 99%

“…FunctionDB is related to constraint databases and constraint programming systems [8,10,15], but in contrast to these systems, which typically strive to find closed form solutions, and are hence slow or intractable for nonlinear constraints, FunctionDB queries return discrete relational-style results intuitive to an end user. Hence, we can leverage approximation to achieve good performance for a wide class of polynomials.…”

Section: Introductionmentioning

confidence: 99%

Querying continuous functions in a database system

Thiagarajan¹,

Madden²

2008

Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data

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Many scientific, financial, data mining and sensor network applications need to work with continuous, rather than discrete data e.g., temperature as a function of location, or stock prices or vehicle trajectories as a function of time. Querying raw or discrete data is unsatisfactory for these applications -e.g., in a sensor network, it is necessary to interpolate sensor readings to predict values at locations where sensors are not deployed. In other situations, raw data can be inaccurate owing to measurement errors, and it is useful to fit continuous functions to raw data and query the functions, rather than raw data itself -e.g., fitting a smooth curve to noisy sensor readings, or a smooth trajectory to GPS data containing gaps or outliers. Existing databases do not support storing or querying continuous functions, short of brute-force discretization of functions into a collection of tuples. We present FunctionDB, a novel database system that treats mathematical functions as first-class citizens that can be queried like traditional relations. The key contribution of FunctionDB is an efficient and accurate algebraic query processor -for the broad class of multi-variable polynomial functions, FunctionDB executes queries directly on the algebraic representation of functions without materializing them into discrete points, using symbolic operations: zero finding, variable substitution, and integration. Even when closed form solutions are intractable, FunctionDB leverages symbolic approximation operations to improve performance. We evaluate FunctionDB on real data sets from a temperature sensor network, and on traffic traces from Boston roads. We show that operating in the functional domain has substantial advantages in terms of accuracy (15-30%) and up to order of magnitude (10x-100x) performance wins over existing approaches that represent models as discrete collections of points.

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“…For more details about 2k-tree construction, we refer the reader to ( (Haroud and Faltings, 1994), (Sam- Haroud, 1995)). …”

Section: K-tree Constructionmentioning

confidence: 99%

“…We show in (Haroud and Faltings, 1994) that PC-2 computes a path-consistent network representation of binary CCSPs in O(n3w 2 log4(w)) where w is the number of feasibility nodes in the largest tree and n is the number of variables. We also propose in (Sam-Haroud, 1995) a variant of Cooper's k-consistency algorithm (Cooper, 1989), adapted to the 2k-tree representation of constraints.…”

Section: Consistency Algorithms Using 2 K-treesmentioning

confidence: 99%

Consistency techniques for continuous constraints

1996

Self Cite

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We consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.Our approach is based on approximating regions of feasible solutions by 2 k-trees, a representation commonly used in computer vision and image processing. We give simple and stable algorithms for computing labelings with arbitrary degrees of consistency. The algorithms can process constraints and solution spaces of arbitrary complexity, but with a fixed maximal resolution.Previous work has shown that when constraints are convex and binary, path-consistency is sufficient to ensure global consistency. We show that for continuous domains, this result can be generalized to ternary and in fact arbitrary n-try constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.

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Global consistency for continuous constraints

Cited by 12 publications

References 10 publications

Interval constraint solving for camera control and motion planning

Interval constraint solving for camera control and motion planning

Querying continuous functions in a database system

Consistency techniques for continuous constraints

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