The Experts below are selected from a list of 51258 Experts worldwide ranked by ideXlab platform
David Steurer - One of the best experts on this subject based on the ideXlab platform.
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an Asymptotic Approximation scheme for multigraph edge coloring
ACM Transactions on Algorithms, 2008Co-Authors: Peter Sanders, David SteurerAbstract:The edge coloring problem considers the assignment of colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, that is, parallel edges are allowed. The best previous algorithms achieve a fixed constant Approximation factor plus a small additive offset. One of our algorithms achieves solution quality opt p s9opt/2 and has execution time polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.
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an Asymptotic Approximation scheme for multigraph edge coloring
Symposium on Discrete Algorithms, 2005Co-Authors: Peter Sanders, David SteurerAbstract:The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges are allowed. The best previous algorithms achieve a fixed constant Approximation factor plus a small additive offset. Our algorithms achieve arbitrarily good Approximation factors at the cost of slightly larger additive terms. In particular, for any ∈ > 0 we achieve a solution quality of (1 + ∈)opt + O(1/∈). The execution times of one algorithm are independent of ∈ and polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.
Peter Sanders - One of the best experts on this subject based on the ideXlab platform.
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an Asymptotic Approximation scheme for multigraph edge coloring
ACM Transactions on Algorithms, 2008Co-Authors: Peter Sanders, David SteurerAbstract:The edge coloring problem considers the assignment of colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, that is, parallel edges are allowed. The best previous algorithms achieve a fixed constant Approximation factor plus a small additive offset. One of our algorithms achieves solution quality opt p s9opt/2 and has execution time polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.
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an Asymptotic Approximation scheme for multigraph edge coloring
Symposium on Discrete Algorithms, 2005Co-Authors: Peter Sanders, David SteurerAbstract:The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges are allowed. The best previous algorithms achieve a fixed constant Approximation factor plus a small additive offset. Our algorithms achieve arbitrarily good Approximation factors at the cost of slightly larger additive terms. In particular, for any ∈ > 0 we achieve a solution quality of (1 + ∈)opt + O(1/∈). The execution times of one algorithm are independent of ∈ and polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.
N Ramanujam - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic numerical method for boundary value problems for singularly perturbed fourth order ordinary differential equations with a weak interior layer
Applied Mathematics and Computation, 2006Co-Authors: V Shanthi, N RamanujamAbstract:Abstract Singularly perturbed two-point boundary value problems (SPBVPs) of convection–diffusion type for fourth-order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative with a discontinuous source term is considered. The given fourth-order BVP is transformed into a system of weakly coupled systems of two second-order ODEs, one without the parameter and the other with the parameter e multiplying the highest derivative, and suitable boundary conditions. In this paper, a computational method for solving this system is presented. In this method, we first find the zero-order Asymptotic Approximation expansion of the solution of the weakly coupled system. Then the system is decoupled by replacing the first component of the solution by its zero-order Asymptotic Approximation expansion of the solution in the second equation. Then the second equation is solved by the numerical method which is constructed for this problem which involves Shishkin mesh.
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computational methods for reaction diffusion problems for fourth order ordinary differential equations with a small parameter at the highest derivative
Applied Mathematics and Computation, 2004Co-Authors: V Shanthi, N RamanujamAbstract:In this paper basically-Asymptotic numerical methods for solving singularly perturbed two-point boundary value problems for fourth order ordinary differential equations of the form-@ey^i^v(x)+b(x)y^'^'(x)+c(x)y(x)=f(x),x@?D:=(0,1),y(0)=p,y^'(0)=q,y^'^'(0)=r,y^'^'(1)=s,is considered. Here a prime ''''' denotes a differentiation with respect to x, b(x), c(x) and f(x) are smooth functions, b(x)>=@b>0, 0>=c(x)>=-@c, @c>0 and 0<@e@?1. The above boundary value problem is transformed into an equivalent weakly coupled system of two first order ordinary differential equations subject to suitable initial conditions and one second order singularly perturbed ordinary differential equations subject to suitable boundary conditions. In order to solve this system three computational methods are suggested in this paper. In these methods, first we find a zero order Asymptotic Approximation of the solution of the weakly coupled system. Then the system is decoupled by replacing the first component of the solution by its zero order Asymptotic Approximation of the solution in the second order equation. Then the second order equation is solved separately by three methods namely fitted operator method, fitted mesh method and boundary value technique. Error estimates are derived and examples are provided to illustrate the methods.
Federico A Bugni - One of the best experts on this subject based on the ideXlab platform.
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comparison of inferential methods in partially identified models in terms of error in coverage probability
Econometric Theory, 2016Co-Authors: Federico A BugniAbstract:This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: the bootstrap, subsampling, and an Asymptotic Approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero.Under certain conditions, we show that the ECP of the bootstrap and the ECP of the Asymptotic Approximation converge to zero at the same rate, which is a faster rate than the rate of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the Asymptotic Approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in nite samples.
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comparison of inferential methods in partially identified models in terms of error in coverage probability
Econometric Theory, 2016Co-Authors: Federico A BugniAbstract:This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: bootstrap, subsampling, and Asymptotic Approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero. Under certain conditions, we show that the ECP of the bootstrap and the ECP of the Asymptotic Approximation converge to zero at the same rate, which is a faster rate than that of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the Asymptotic Approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in finite samples.
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a comparison of inferential methods in partially identified models in terms of error in the coverage probability
Social Science Research Network, 2011Co-Authors: Federico A BugniAbstract:This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: the bootstrap, subsampling, and an Asymptotic Approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero.Under certain conditions, we show that the ECP of the bootstrap and the ECP of the Asymptotic Approximation converge to zero at the same rate, which is a faster rate than the rate of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the Asymptotic Approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in nite samples.
Richard G. Baraniuk - One of the best experts on this subject based on the ideXlab platform.
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Representation and Compression of Multidimensional Piecewise Functions Using Surflets
IEEE Transactions on Information Theory, 2009Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, Approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal Asymptotic Approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. Our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth Approximation. Both of these schemes achieve the optimal Asymptotic Approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide Asymptotic performance results for both discrete function spaces and relate this Asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For Approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based coders and previously studied Approximation schemes based on wedgelets and wavelets.
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Sparse sign...
2008Co-Authors: Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, Approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal Asymptotic Approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. Our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth Approximation. Both of these schemes achieve the optimal Asymptotic Approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
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Representation and compression of multi-dimensional piecewise functions using surflets
2006Co-Authors: Venkat Chandrasekaran, Michael B. Wakin, Dror Baron, Richard G. BaraniukAbstract:We study the representation, Approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M − 1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal Asymptotic Approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. Our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth Approximation. Both of these schemes achieve the optimal Asymptotic Approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the correspondin
