The Experts below are selected from a list of 141 Experts worldwide ranked by ideXlab platform
Rina Dechter - One of the best experts on this subject based on the ideXlab platform.
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Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems
Constraints, 2003Co-Authors: Javier Larrosa, Rina DechterAbstract:There are two main solving schemas for constraint satisfaction and optimization problems : i ) search , whose basic step is branching over the values of a variables, and ii ) dynamic programming , whose basic step is variable elimination. Variable elimination is time and Space Exponential in a graph parameter called induced width, which renders the approach infeasible for many problem classes. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables may reduce drastically the search tree size. In this paper we introduce BE-BB( k ), a hybrid general algorithm that combines search and variable elimination. The parameter k controls the tradeoff between the two strategies. The algorithm is Space Exponential in k . Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in constraint satisfaction, Max-CSP and Weighted CSP. Especially in optimization tasks, the advantage of our approach over plain search can be overwhelming.
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bucket elimination a unifying framework for reasoning
Artificial Intelligence, 1999Co-Authors: Rina DechterAbstract:Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problem-solving and reasoning tasks. Algorithms such as directional-resolution for propositional satisfiability, adaptive-consistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucket-elimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and Space Exponential in the inducedwidth of the problem’s interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called “conditioning search” require only linear Space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set ,o r acutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucket-elimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade Space for time. © 1999 Elsevier Science B.V. All rights reserved.
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Bucket elimination: A unifying framework for reasoning
Artificial Intelligence, 1999Co-Authors: Rina DechterAbstract:AbstractBucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problem-solving and reasoning tasks. Algorithms such as directional-resolution for propositional satisfiability, adaptive-consistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucket-elimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and Space Exponential in the induced-width of the problem's interaction graph.While elimination strategies have extensive demands on memory, a contrasting class of algorithms called “conditioning search” require only linear Space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization).The paper presents the bucket-elimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade Space for time
Javier Larrosa - One of the best experts on this subject based on the ideXlab platform.
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Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems
Constraints, 2003Co-Authors: Javier Larrosa, Rina DechterAbstract:There are two main solving schemas for constraint satisfaction and optimization problems : i ) search , whose basic step is branching over the values of a variables, and ii ) dynamic programming , whose basic step is variable elimination. Variable elimination is time and Space Exponential in a graph parameter called induced width, which renders the approach infeasible for many problem classes. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables may reduce drastically the search tree size. In this paper we introduce BE-BB( k ), a hybrid general algorithm that combines search and variable elimination. The parameter k controls the tradeoff between the two strategies. The algorithm is Space Exponential in k . Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in constraint satisfaction, Max-CSP and Weighted CSP. Especially in optimization tasks, the advantage of our approach over plain search can be overwhelming.
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boosting search with variable elimination
Lecture Notes in Computer Science, 2000Co-Authors: Javier LarrosaAbstract:Variable elimination is the basic step of Adaptive Consistency[4]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its Exponential Space and time complexity. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables, reduces the search tree size. In this paper we introduce VarElimSearch(S,k), a hybrid metaalgorithm that combines search and variable elimination. The parameter S names the particular search procedure and k controls the tradeoff between the two strategies. The algorithm is Space Exponential in k. Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We also provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in binary sparse problems. Experiments cover the tasks of finding one solution and the best solution (Max-CSP). Specially in the Max-CSP case, the advantage of our approach can be overwhelming.
Gregory B. Sorkin - One of the best experts on this subject based on the ideXlab platform.
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ICALP (1) - Separate, Measure and Conquer: Faster Polynomial-Space Algorithms for Max 2-CSP and Counting Dominating Sets
Automata Languages and Programming, 2015Co-Authors: Serge Gaspers, Gregory B. SorkinAbstract:We show a method resulting in the improvement of several polynomial-Space, Exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, such as Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for an improved running time analysis.
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SEPARATE, MEASURE AND CONQUER: FASTER ALGORITHMS FOR MAX 2-CSP AND COUNTING DOMINATING SETS
arXiv: Data Structures and Algorithms, 2014Co-Authors: Serge Gaspers, Gregory B. SorkinAbstract:We show a method resulting in the improvement of several polynomial-Space, Exponential-time algorithms. An instance of the problem Max (r,2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n (vertices in the constraint graph G), and the number of constraints m (edges in G). When G is cubic, and omitting sub-Exponential terms here for clarity, we give an algorithm running in time r (1/5) n = r (2/15) m ; the previous best was r (1/4) n = r (1/6) m . By known results, this improvement for the cubic case results in an algorithm running in time r (9/50) m for general instances; the previous best was r (19/100) m . We show that the analysis of the earlier algorithm was tight: our improvement is in the algorithm, not just the analysis. The new algorithm, like the old, extends to Polynomial and Ring CSP (encompassing graph bisection, the Ising model, and counting). It is also the fastest polynomial- Space algorithm for Max Cut, for cubic and general instances. We also give faster algorithms for #Dominating Set, counting the dominating sets of every cardinality 0,...,n for a graph G of order n. For cubic graphs, our algorithm runs in time 3 (1/6) n ; the previous best was 2 (1/2) n . For general graphs, we give an unrelated algorithm running in time 1.5183 n ; the previous best was 1.5673 n . The previous best algorithms for these problems all used local transformations and were an- alyzed by the "Measure and Conquer" method. Our new algorithms capitalize on the existence of small balanced separators for cubic graphs — a non-local property — and the ability to tailor the local algorithms always to "pivot" on a vertex in the separator. The new algorithms perform much as the old ones until the separator is empty, at which point they gain because the remaining vertices are split into two independent problem instances that can be solved recursively. It is likely that such algorithms can be effective for other problems too, and we present their design and analysis in a general framework.
Rik W. De Doncker - One of the best experts on this subject based on the ideXlab platform.
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IECON - Agent-Based Voltage Regulation Scheme for Active Distributed Networks under Distributed Quantized Communication
IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, 2019Co-Authors: Xiaoqing Lu, Antonello Monti, Rik W. De DonckerAbstract:In this paper, a novel distributed pinning control scheme for the voltage regulation of active distributed networks through limited bandwidth communication. In actual active distributed networks, the information exchange among multiple and cooperative DGs may be subject to these constraints of communication bandwidth and storage Space, DGs can only receive uniform quantized information. Towards that end, a distributed pinning control scheme will synchronize the terminal voltage of DGs to their reference value by a virtual leader through sparse communication considering communication band- width and storage Space Exponential convergence. By means of the Gronwall's inequality tools and algebraic graph theory, distributed pinning protocols are developed to be employed for active distributed networks, in which manner the criteria for the stability analysis to maintain the closed-loop system stable are derived. Simulation results on an active distributed network system are provided to show the effectiveness of the proposed control protocols.
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Agent-Based Voltage Regulation Scheme for Active Distributed Networks under Distributed Quantized Communication
IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, 2019Co-Authors: Xiaoqing Lu, Antonello Monti, Rik W. De DonckerAbstract:In this paper, a novel distributed pinning control scheme for the voltage regulation of active distributed networks through limited bandwidth communication. In actual active distributed networks, the information exchange among multiple and cooperative DGs may be subject to these constraints of communication bandwidth and storage Space, DGs can only receive uniform quantized information. Towards that end, a distributed pinning control scheme will synchronize the terminal voltage of DGs to their reference value by a virtual leader through sparse communication considering communication band- width and storage Space Exponential convergence. By means of the Gronwall's inequality tools and algebraic graph theory, distributed pinning protocols are developed to be employed for active distributed networks, in which manner the criteria for the stability analysis to maintain the closed-loop system stable are derived. Simulation results on an active distributed network system are provided to show the effectiveness of the proposed control protocols.
Jean-marc Mercier - One of the best experts on this subject based on the ideXlab platform.
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Mesh-free error integration in arbitrary dimensions: A numerical study of discrepancy functions
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Philippe G. Lefloch, Jean-marc MercierAbstract:Abstract We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel Space. A kernel typically captures regularity and qualitative properties of functions “beyond” the standard Sobolev regularity class. We are interested in the issue whether quantitative error bounds can be a priori guaranteed in applications (including mathematical finance, scientific computing, and machine learning). Our main contribution is a numerical study of the error discrepancy function based on a comparison between several numerical strategies, when one varies the choice of the kernel, the number of approximation points, and the dimension of the problem. We consider two strategies in order to localize to a bounded set the standard kernels defined in the whole Euclidian Space (Exponential, multiquadric, Gaussian, truncated), namely, on one hand the class of periodic kernels defined via a discrete Fourier transform on a lattice and, on the other hand, a class of transport-based kernels. Relying on the Poisson formula on a lattice together with heuristic arguments, we study the derivation of theoretical bounds for the discrepancy function of periodic kernels. Then, for four kernels of particular interest we perform extensive numerical experiments and generate the optimal distributions of points and the discrepancy error functions. Our numerical results validate our theoretical observations and, importantly, provide us with quantitative estimates for the error made with a kernel-based strategy as opposed to a purely random strategy.
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Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions
arXiv: Analysis of PDEs, 2019Co-Authors: Philippe G. Lefloch, Jean-marc MercierAbstract:We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel Space. A kernel typically captures regularity and qualitative properties of functions "beyond" the standard Sobolev regularity class. We are interested in the issue whether quantitative error bounds can be a priori guaranteed in applications (e.g.~scientific computing, mathematical finance, machine learning). Our main contribution is a numerical study of the error discrepancy function when one varies the choice of the kernel, the number of approximation points, and the dimension of the problem. We consider here wo strategies in order to localize to a bounded set the standard kernels defined in the whole Euclidian Space (Exponential, multiquadric, Gaussian, truncated), namely, on one hand the class of periodic kernels defined via a discrete Fourier transform on a lattice, and on the other hand the class of transported kernels with compact support. First of all, based on heuristic arguments and using on a Poisson formula on a lattice, we derive theoretical bounds satisfied by the discrepancy function for periodic kernels. Second, for each kernel of Exponential, multiquadric, Gaussian, truncated type, we perform the extensive numerical experiments required in order to generate the optimal distributions of points and the discrepancy functions. Our numerical results provide us with quantitative estimates of the error made with kernel-based strategy vs. a purely random strategy, and also validate our theoretical analysis.