The Experts below are selected from a list of 25117656 Experts worldwide ranked by ideXlab platform
Amit Kumar - One of the best experts on this subject based on the ideXlab platform.
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constant factor approximation algorithm for weighted flow time on a single machine in pseudo polynomial time
Foundations of Computer Science, 2018Co-Authors: Jatin Batra, Naveen Garg, Amit KumarAbstract:In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The algorithm also extends directly to the problem of minimizing the _p norm of weighted flow-times. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call Demand MultiCut problem. Even though we do not give a constant factor approximation algorithm for the Demand MultiCut problem on trees, we show that the specific instances of Demand MultiCut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.
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constant factor approximation algorithm for weighted flow time on a single machine in pseudo polynomial time
arXiv: Data Structures and Algorithms, 2018Co-Authors: Amit Kumar, Jatin Batra, Naveen GargAbstract:In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call the Demand Multi-Cut problem. Even though we do not give a constant factor approximation algorithm for the Demand Multi-Cut problem on trees, we show that the specific instances of Demand Multi-Cut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.
Bálint Joó - One of the best experts on this subject based on the ideXlab platform.
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parton distribution functions from ioffe time pseudodistributions from lattice calculations approaching the physical point
Physical Review Letters, 2020Co-Authors: Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, D G Richards, Savvas ZafeiropoulosAbstract:We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudo-distributions. Beyond the reconstruction of the Bjorken-$x$ dependence we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudo-distribution. We compare our findings with the pertinent phenomenological determinations.
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Parton Distribution Functions from Ioffe time pseudo-distributions
JHEP, 2019Co-Authors: Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, David Richards, Savvas ZafeiropoulosAbstract:In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution func- tions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume ex- trapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.
Savvas Zafeiropoulos - One of the best experts on this subject based on the ideXlab platform.
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parton distribution functions from ioffe time pseudodistributions from lattice calculations approaching the physical point
Physical Review Letters, 2020Co-Authors: Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, D G Richards, Savvas ZafeiropoulosAbstract:We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudo-distributions. Beyond the reconstruction of the Bjorken-$x$ dependence we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudo-distribution. We compare our findings with the pertinent phenomenological determinations.
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Parton Distribution Functions from Ioffe time pseudo-distributions
JHEP, 2019Co-Authors: Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, David Richards, Savvas ZafeiropoulosAbstract:In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution func- tions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume ex- trapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.
Sergei Tabachnikov - One of the best experts on this subject based on the ideXlab platform.
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pseudo riemannian geodesics and billiards
Advances in Mathematics, 2009Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Abstract In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generalizations. We also introduce and study pseudo-Euclidean billiards, emphasizing their distinction from Euclidean ones. We present a pseudo-Euclidean version of the Clairaut theorem on geodesics on surfaces of revolution. We prove pseudo-Euclidean analogs of the Jacobi–Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
arXiv: Differential Geometry, 2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
arXiv: Differential Geometry, 2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
Jatin Batra - One of the best experts on this subject based on the ideXlab platform.
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constant factor approximation algorithm for weighted flow time on a single machine in pseudo polynomial time
Foundations of Computer Science, 2018Co-Authors: Jatin Batra, Naveen Garg, Amit KumarAbstract:In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The algorithm also extends directly to the problem of minimizing the _p norm of weighted flow-times. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call Demand MultiCut problem. Even though we do not give a constant factor approximation algorithm for the Demand MultiCut problem on trees, we show that the specific instances of Demand MultiCut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.
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constant factor approximation algorithm for weighted flow time on a single machine in pseudo polynomial time
arXiv: Data Structures and Algorithms, 2018Co-Authors: Amit Kumar, Jatin Batra, Naveen GargAbstract:In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call the Demand Multi-Cut problem. Even though we do not give a constant factor approximation algorithm for the Demand Multi-Cut problem on trees, we show that the specific instances of Demand Multi-Cut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.
