J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....implicitly generates the universal constraint. Applying adaptive consistency to linear constraints and processing each pair of relevant inequalities in a bucket by linear elimination yields a bucket elimination algorithm which coincides with the well known Fourier elimination algorithm (see [30]) From the general principle of variable elimination, and as is already known, the algorithm decides the solvability of any set of linear inequalities over the rationals and generates a problem representation which is backtrack free. The algorithm expressed as a bucket elimination algorithm is ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....problem solving and reasoning activities. Among the algorithms that can be expressed as bucket elimination are directional resolution for propositional satisfiability [23, 50] adaptive consistency for constraint satisfaction [22] Fourier and Gaussian elimination for linear inequalities 2 [37], dynamic programming for combinatorial optimization [3] as well as many algorithms for probabilistic inference [20] In all these areas problems are represented by a set of variables and a set of dependencies (e.g. constraints, cost functions, or probabilities) whose structure can be captured ....

....bucket elimination algorithms within a single principled framework. The bucket elimination framework [20] provides a convenient and succinct language for expressing elimination algorithms in many areas. In addition to dynamic programming [3] constraint satisfaction [22] and Fourier elimination [37], there are variations on these ideas and algorithms for probabilistic inference [7, 57, 55, 59] Our approach is inspired by adaptive consistency, a full bucket elimination algorithm whose approximation, directional i consistency and its relational variant directional relationalconsistency ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....complex problem solving and reasoning activities. Among the algorithms that can be accommodated within this framework are directional resolution for propositional satisfiability [18] adaptive consistency for constraint satisfaction [17] Fourier and Gaussian elimination for linear inequalities [28], dynamic programming for combinatorial optimization [3] as well as many algorithms for probabilistic inference [13] In all these areas, problems are represented by a set of discrete variables, and by a set of dependencies (e.g. constraints, cost functions, and probabilities) that can be ....

....all bucketelimination algorithms within a single principled idea. The bucket elimination framework [13] provides a convenient and succinct language for expressing elimination algorithms in many areas. In addition to dynamic programming [3] constraint satisfaction [17] and Fourier elimination [28], there are variations on these ideas and algorithms for probabilistic inference [5, 50, 48, 51] Mini bucket al..gorithms parallel directional local consistency enforcing algorithms for constraint processing. Specifically, adaptive consistency is a full bucket elimination algorithm whose ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....complex problem solving and reasoning activities. Among the algorithms that can be expressed as bucket elimination are directional resolution for propositional satisfiability [18] adaptiveconsistency for constraint satisfaction [17] Fourier and Gaussian elimination for linear inequalities [28], dynamic programming for combinatorial optimization [3] as well as many algorithms for probabilistic inference [13] In all these areas, problems are represented by a set of discrete variables, and by a set of dependencies (e.g. constraints, cost functions, and probabilities) that can be ....

....all bucketelimination algorithms within a single principled idea. The bucket elimination framework [13] provides a convenient and succinct language for expressing elimination algorithms in many areas. In addition to dynamic programming [3] constraint satisfaction [17] and Fourier elimination [28], there are variations on these ideas and algorithms for probabilistic inference [5, 50, 48, 51] Mini bucket al..gorithms parallel directional local consistency enforcing algorithms for constraint processing. Specifically, adaptive consistency is a full bucket elimination algo24 rithm whose ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992. 63

....complex problem solving and reasoning activities. Among the algorithms that can be accommodated within this framework are directional resolution for propositional satisfiability [18] adaptive consistency for constraint satisfaction [17] Fourier and Gaussian elimination for linear inequalities [28], dynamic programming for combinatorial optimization [3] as well as many algorithms for probabilistic inference [13] In all these areas, problems are represented by a set of discrete variables, and by a set of dependencies (e.g. constraints, cost functions, and probabilities) that can be ....

....all bucketelimination algorithms within a single principled idea. The bucket elimination framework [13] provides a convenient and succinct language for expressing elimination algorithms in many areas. In addition to dynamic programming [3] constraint satisfaction [17] and Fourier elimination [28], there are variations on these ideas and algorithms for probabilistic inference [5, 50, 48, 51] Mini bucket al..gorithms parallel directional local consistency enforcing algorithms for constraint processing. Specifically, adaptive consistency is a full bucket elimination algorithm whose ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....implicitly generates the universal constraint. Applying adaptive consistency to linear constraints and processing each pair of relevant inequalities in a bucket by linear elimination, yields a bucket elimination algorithm which coincides with well known Fourier elimination algorithm (see [32]) From the general principle of variable elimination and as is already known the algorithm decides the solvability of any set of linear inequalities over the rationals, and generates a problem representation which is backtrack free. The algorithm expressed as a bucket elimination algorithm is ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....complex problem solving and reasoning activities. Among the algorithms that can be expressed as bucket elimination are directional resolution for propositional satisfiability [19] adaptiveconsistency for constraint satisfaction [18] Fourier and Gaussian elimination for linear inequalities [31], dynamic programming for combinatorial optimization [3] as well as many algorithms for probabilistic inference [14] In all these areas problems are represented by a set of variables and by a set of dependencies (e.g. constraints, cost functions, and probabilities) that can be captured by a ....

....bucket elimination algorithms within a single principled framework. The bucket elimination framework [14] provides a convenient and succinct language for expressing elimination algorithms in many areas. In addition to dynamic programming [3] constraint satisfaction [18] and Fourier elimination [31], there are variations on these ideas and algorithms for probabilistic inference [5, 53, 51, 55] Mini bucket al..gorithms parallel directional local consistency enforcing algorithms for constraint processing. Our approach is inspired by adaptive consistency, a full bucketelimination algorithm whose ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....ff and fi. It is unclear, though, that there is an integer extension to x r which is the reason for partial containment. 2. Incorporating linear elimination into DRC 3 results in algorithm Directional Linear Elimination (abbreviated DLE) which is the well known Fourier elimination algorithm (see [16]) It was shown that the algorithm decides the solvability of any set of linear inequalities over the Reals. Directional Linear Elimination ( o) 1. Initialize: generate an ordered partition of the inequalities into buckets. 2. for i n downto 1 3. do for each pair fff; fig bucket i , ....

J-L Lassez and M. Mahler, "On Fourier's algorithm for linear constraints" Journal of Automated Reasoning, Vol 9, 1992.

.... Among the algorithms that can be accommodated within this framework are directional resolution for propositional satisfiability [ Dechter and Rish, 1994 ] adaptive consistency for constraint satisfaction [ Dechter and Pearl, 1987 ] Fourier and Gaussian elimination for linear inequalities [ Lassez and Mahler, 1992 ] and dynamic programming for combinatorial optimization [ Bertele and Brioschi, 1972 ] Many algorithms for probabilistic inference, such as belief updating, finding the most probable explanation, finding the maximum a posteriori hypothesis, and computing the maximum expected utility, also ....

....provides a convenient and succinct language in which to express elimination algorithms across many areas. Most of these algorithms are widely known. In addition to dynamic programming [ Bertele and Brioschi, 1972 ] constraint satisfaction [ Dechter and Pearl, 1987 ] and Fourier elimination [ Lassez and Mahler, 1992 ] there are variations on these ideas and algorithms for probabilistic inference in [ Canning et al. 1978; Tatman and Shachter, 1990; Shenoy, 1992; Zhang and Poole, 1996 ] Mini bucket approximation algorithms parallel consistency enforcing algorithms for constraint processing, in particular ....

J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

....linear inequalities can be globally solved by DRC 2 . Incorporating linear elimination into DRC 2 (when the constraints are presented as linear inequalities) results in algorithm Directional Linear Elimination (abbreviated DLE) which is the well known Fourier elimination algorithm (see [28]) Indeed, as dictated by our theory and as is already known the algorithm decides the solvability of any set of linear inequalities over the Rationals. Directional Linear Elimination ( o) Input: A set of linear inequalities , an ordering o = x 1 ; xn of its variables. Output: A ....

J-L Lassez and M. Mahler, "On Fourier's algorithm for linear constraints" Journal of Automated Reasoning, Vol 9, 1992.

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J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

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J.-L. Lassez and M. J. Mahler. On Fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9(3):373-379, 1992.

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Jean-Louis Lassez and Michael J. Mahler. On Fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9(3):373--379, 1992.

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J.-L. Lassez and M. Mahler. On fourier's algorithm for linear constraints. Journal of Automated Reasoning, 9, 1992.

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