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Vangelis Th. Paschos - One of the best experts on this subject based on the ideXlab platform.
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Upper Dominating Set: Tight Algorithms for Pathwidth and Sub-Exponential Approximation.
arXiv: Data Structures and Algorithms, 2021Co-Authors: Louis Dublois, Michael Lampis, Vangelis Th. PaschosAbstract:An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper Dominating Set}, as well as its sub-Exponential Approximation. First, we prove that, under ETH, \textsc{$k$-Upper Dominating Set} cannot be solved in time $O(n^{o(k)})$ (improving on $O(n^{o(\sqrt{k})})$), and in the same time we show under the same complexity assumption that for any constant ratio $r$ and any $\varepsilon > 0$, there is no $r$-Approximation algorithm running in time $O(n^{k^{1-\varepsilon}})$. Then, we settle the problem's complexity parameterized by pathwidth by giving an algorithm running in time $O^*(6^{pw})$ (improving the current best $O^*(7^{pw})$), and a lower bound showing that our algorithm is the best we can get under the SETH. Furthermore, we obtain a simple sub-Exponential Approximation algorithm for this problem: an algorithm that produces an $r$-Approximation in time $n^{O(n/r)}$, for any desired Approximation ratio $r 1$ and $\varepsilon > 0$, no algorithm can output an $r$-Approximation in time $n^{(n/r)^{1-\varepsilon}}$. Hence, we completely characterize the approximability of the problem in sub-Exponential time.
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Upper Dominating Set: Tight Algorithms for Pathwidth and Sub-Exponential Approximation
2021Co-Authors: Dublois Louis, Lampis Michael, Vangelis Th. PaschosAbstract:An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper Dominating Set}, as well as its sub-Exponential Approximation. First, we prove that, under ETH, \textsc{$k$-Upper Dominating Set} cannot be solved in time $O(n^{o(k)})$ (improving on $O(n^{o(\sqrt{k})})$), and in the same time we show under the same complexity assumption that for any constant ratio $r$ and any $\varepsilon > 0$, there is no $r$-Approximation algorithm running in time $O(n^{k^{1-\varepsilon}})$. Then, we settle the problem's complexity parameterized by pathwidth by giving an algorithm running in time $O^*(6^{pw})$ (improving the current best $O^*(7^{pw})$), and a lower bound showing that our algorithm is the best we can get under the SETH. Furthermore, we obtain a simple sub-Exponential Approximation algorithm for this problem: an algorithm that produces an $r$-Approximation in time $n^{O(n/r)}$, for any desired Approximation ratio $r < n$. We finally show that this time-Approximation trade-off is tight, up to an arbitrarily small constant in the second exponent: under the randomized ETH, and for any ratio $r > 1$ and $\varepsilon > 0$, no algorithm can output an $r$-Approximation in time $n^{(n/r)^{1-\varepsilon}}$. Hence, we completely characterize the approximability of the problem in sub-Exponential time.Comment: This paper has been accepted to CIAC 202
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Exponential Approximation schemata for some network design problems
Journal of Discrete Algorithms, 2013Co-Authors: Nicolas Boria, Nicolas Bourgeois, Bruno Escoffier, Vangelis Th. PaschosAbstract:We study Approximation of some well-known network design problems such as the traveling salesman problem (for both minimization and maximization versions) and the min steiner tree problem by moderately Exponential algorithms. The general goal of the issue of moderately Exponential Approximation is to catch up on polynomial inapproximability by designing superpolynomial algorithms achieving Approximation ratios unachievable in polynomial time. Worst-case running times of such algorithms are significantly smaller than those needed for optimal solutions of the problems handled.
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Exponential Approximation schemata for some network design problems
Journal of Discrete Algorithms, 2013Co-Authors: Nicolas Boria, Nicolas Bourgeois, Bruno Escoffier, Vangelis Th. PaschosAbstract:We study Approximation of some well-known network design problems such as traveling salesman problem (for both minimization and maximization versions) and min steiner tree, by moderately Exponential algorithms. The general goal of the issue of moderately Exponential Approximationis to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-caserunning times importantly smaller than those needed for exact computation, Approximation ratiosunachievable in polynomial time.
Adrian Röllin - One of the best experts on this subject based on the ideXlab platform.
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New rates for Exponential Approximation and the theorems of Rényi and Yaglom
The Annals of Probability, 2011Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:We introduce two abstract theorems that reduce a variety of complex Exponential distributional Approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of Renyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the Exponential asymptotic behavior of a critical Galton–Watson process conditioned on nonextinction. The primary tools are an adaptation of Stein’s method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.
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Exponential Approximation for the Nearly Critical Galton-Watson Process and Occupation Times of Markov Chains
Electronic Journal of Probability, 2011Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:In this article we provide new applications for Exponential Approximation using the framework of Pekoz and Rollin (2011), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new Exponential Approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erdos-Taylor theorem.
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Exponential Approximation for the nearly critical Galton-Watson process and occupation times of Markov chains
arXiv: Probability, 2010Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:In this article we provide new applications for Exponential Approximation using the framework of Pek\"oz and R\"ollin (in press), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new Exponential Approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erd\H{o}s-Taylor theorem.
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new rates for Exponential Approximation and the theorems of r e nyi and yaglom
arXiv: Probability, 2009Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:We introduce two abstract theorems that reduce a variety of complex Exponential distributional Approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of R\'{e}nyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the Exponential asymptotic behavior of a critical Galton--Watson process conditioned on nonextinction. The primary tools are an adaptation of Stein's method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.
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Exponential Approximation by Stein's Method and Spectral Graph Theory
arXiv: Probability, 2006Co-Authors: Sourav Chatterjee, Jason Fulman, Adrian RöllinAbstract:General Berry-Esseen bounds are developed for the Exponential distri- bution using Stein's method and a new concentration inequality approach. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Johnson graph has an Exponential limit.
Amin Saberi - One of the best experts on this subject based on the ideXlab platform.
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simply Exponential Approximation of the permanent of positive semidefinite matrices
Foundations of Computer Science, 2017Co-Authors: Nima Anari, Leonid Gurvits, Shayan Oveis Gharan, Amin SaberiAbstract:We design a deterministic polynomial time cn Approximation algorithm for the permanent of positive semidefinite matrices where c = e+1 ⋍ 4:84. We write a natural convex relaxation and show that its optimum solution gives a cn Approximation of the permanent. We further show that this factor is asymptotically tight by constructing a family of positive semidefinite matrices. We also show that our result implies an approximate version of the permanent-ontop conjecture, which was recently refuted in its original form; we show that the permanent is within a cn factor of the top eigenvalue of the Schur power matrix.
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Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices
arXiv: Combinatorics, 2017Co-Authors: Nima Anari, Leonid Gurvits, Shayan Oveis Gharan, Amin SaberiAbstract:We design a deterministic polynomial time $c^n$ Approximation algorithm for the permanent of positive semidefinite matrices where $c=e^{\gamma+1}\simeq 4.84$. We write a natural convex relaxation and show that its optimum solution gives a $c^n$ Approximation of the permanent. We further show that this factor is asymptotically tight by constructing a family of positive semidefinite matrices.
Erol A. Peköz - One of the best experts on this subject based on the ideXlab platform.
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New rates for Exponential Approximation and the theorems of Rényi and Yaglom
The Annals of Probability, 2011Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:We introduce two abstract theorems that reduce a variety of complex Exponential distributional Approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of Renyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the Exponential asymptotic behavior of a critical Galton–Watson process conditioned on nonextinction. The primary tools are an adaptation of Stein’s method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.
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Exponential Approximation for the Nearly Critical Galton-Watson Process and Occupation Times of Markov Chains
Electronic Journal of Probability, 2011Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:In this article we provide new applications for Exponential Approximation using the framework of Pekoz and Rollin (2011), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new Exponential Approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erdos-Taylor theorem.
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Exponential Approximation for the nearly critical Galton-Watson process and occupation times of Markov chains
arXiv: Probability, 2010Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:In this article we provide new applications for Exponential Approximation using the framework of Pek\"oz and R\"ollin (in press), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new Exponential Approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erd\H{o}s-Taylor theorem.
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new rates for Exponential Approximation and the theorems of r e nyi and yaglom
arXiv: Probability, 2009Co-Authors: Erol A. Peköz, Adrian RöllinAbstract:We introduce two abstract theorems that reduce a variety of complex Exponential distributional Approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of R\'{e}nyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the Exponential asymptotic behavior of a critical Galton--Watson process conditioned on nonextinction. The primary tools are an adaptation of Stein's method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.
Nima Anari - One of the best experts on this subject based on the ideXlab platform.
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simply Exponential Approximation of the permanent of positive semidefinite matrices
Foundations of Computer Science, 2017Co-Authors: Nima Anari, Leonid Gurvits, Shayan Oveis Gharan, Amin SaberiAbstract:We design a deterministic polynomial time cn Approximation algorithm for the permanent of positive semidefinite matrices where c = e+1 ⋍ 4:84. We write a natural convex relaxation and show that its optimum solution gives a cn Approximation of the permanent. We further show that this factor is asymptotically tight by constructing a family of positive semidefinite matrices. We also show that our result implies an approximate version of the permanent-ontop conjecture, which was recently refuted in its original form; we show that the permanent is within a cn factor of the top eigenvalue of the Schur power matrix.
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Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices
arXiv: Combinatorics, 2017Co-Authors: Nima Anari, Leonid Gurvits, Shayan Oveis Gharan, Amin SaberiAbstract:We design a deterministic polynomial time $c^n$ Approximation algorithm for the permanent of positive semidefinite matrices where $c=e^{\gamma+1}\simeq 4.84$. We write a natural convex relaxation and show that its optimum solution gives a $c^n$ Approximation of the permanent. We further show that this factor is asymptotically tight by constructing a family of positive semidefinite matrices.
