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    • 3. 发明申请
    • DETERMINISTIC WAVELET THRESHOLDING FOR GENERAL-ERROR METRICS
    • 用于一般错误度量的确定性小波变换
    • US20100115350A1
    • 2010-05-06
    • US12605795
    • 2009-10-26
    • Minos N. GarofalakisAmit Kumar
    • Minos N. GarofalakisAmit Kumar
    • G06F11/00
    • G06F17/148
    • Novel, computationally efficient schemes for deterministic wavelet thresholding with the objective of optimizing maximum-error metrics are provided. An optimal low polynomial-time algorithm for one-dimensional wavelet thresholding based on a new dynamic-programming (DP) formulation is provided that can be employed to minimize the maximum relative or absolute error in the data reconstruction. Directly extending a one-dimensional DP algorithm to multi-dimensional wavelets results in a super-exponential increase in time complexity with the data dimensionality. Thus, novel, polynomial-time approximation schemes (with tunable approximation guarantees for the target maximum-error metric) for deterministic wavelet thresholding in multiple dimensions are also provided.
    • 提供了用于确定性小波阈值的计算有效方案,其目的是优化最大误差度量。 提供了一种基于新动态规划(DP)公式的一维小波阈值优化的最优低次多项式时间算法,可用于最小化数据重构中的最大相对误差或绝对误差。 将一维DP算法直接扩展为多维小波导致数据维度在时间复杂度方面的超指数增长。 因此,还提供了用于确定性小波阈值在多个维度中的新颖多项式时间近似方案(对于目标最大误差度量具有可调近似保证)。
    • 4. 发明授权
    • Deterministic wavelet thresholding for general-error metrics
    • 一般误差度量的确定性小波阈值
    • US08055088B2
    • 2011-11-08
    • US12605795
    • 2009-10-26
    • Minos N. GarofalakisAmit Kumar
    • Minos N. GarofalakisAmit Kumar
    • G06K9/00
    • G06F17/148
    • Novel, computationally efficient schemes for deterministic wavelet thresholding with the objective of optimizing maximum-error metrics are provided. An optimal low polynomial-time algorithm for one-dimensional wavelet thresholding based on a new dynamic-programming (DP) formulation is provided that can be employed to minimize the maximum relative or absolute error in the data reconstruction. Directly extending a one-dimensional DP algorithm to multi-dimensional wavelets results in a super-exponential increase in time complexity with the data dimensionality. Thus, novel, polynomial-time approximation schemes (with tunable approximation guarantees for the target maximum-error metric) for deterministic wavelet thresholding in multiple dimensions are also provided.
    • 提供了用于确定性小波阈值的计算有效方案,其目的是优化最大误差度量。 提供了一种基于新动态规划(DP)公式的一维小波阈值优化的最优低次多项式时间算法,可用于最小化数据重构中的最大相对误差或绝对误差。 将一维DP算法直接扩展为多维小波导致数据维度在时间复杂度方面的超指数增长。 因此,还提供了用于确定性小波阈值在多个维度中的新颖多项式时间近似方案(对于目标最大误差度量具有可调近似保证)。
    • 5. 发明授权
    • Deterministic wavelet thresholding for general-error metrics
    • 一般误差度量的确定性小波阈值
    • US07693335B2
    • 2010-04-06
    • US11152842
    • 2005-06-13
    • Minos N. GarofalakisAmit Kumar
    • Minos N. GarofalakisAmit Kumar
    • G06K9/46
    • G06F17/148
    • Novel, computationally efficient schemes for deterministic wavelet thresholding with the objective of optimizing maximum-error metrics are provided. An optimal low polynomial-time algorithm for one-dimensional wavelet thresholding based on a new dynamic-programming (DP) formulation is provided that can be employed to minimize the maximum relative or absolute error in the data reconstruction. Directly extending a one-dimensional DP algorithm to multi-dimensional wavelets results in a super-exponential increase in time complexity with the data dimensionality. Thus, novel, polynomial-time approximation schemes (with tunable approximation guarantees for the target maximum-error metric) for deterministic wavelet thresholding in multiple dimensions are also provided.
    • 提供了用于确定性小波阈值的计算有效方案,其目的是优化最大误差度量。 提供了一种基于新动态规划(DP)公式的一维小波阈值优化的最优低次多项式时间算法,可用于最小化数据重构中的最大相对误差或绝对误差。 将一维DP算法直接扩展为多维小波导致数据维度在时间复杂度方面的超指数增长。 因此,还提供了用于确定性小波阈值在多个维度中的新颖多项式时间近似方案(对于目标最大误差度量具有可调近似保证)。
    • 7. 发明授权
    • Method and apparatus for routing a packet within a plurality of nodes arranged in a line or a tree given a maximum stack depth
    • 用于路由布置在具有最大堆栈深度的一行或一棵树中的多个节点内的分组的方法和装置
    • US07542470B2
    • 2009-06-02
    • US10404010
    • 2003-03-31
    • Anupam GuptaAmit KumarRajeev Rastogi
    • Anupam GuptaAmit KumarRajeev Rastogi
    • H04L12/56
    • H04L45/50H04L45/10H04L45/48
    • A method and apparatus are provided for routing a packet within a plurality of n nodes arranged in a line or tree (or a combination of the foregoing), given a maximum stack depth, s. A fixed stack process for routing packets on a line given a stack depth, s, initially divides a line of n nodes into segments, such as n1/s approximately equal segments. A unique label is assigned to each segment and, within each segment, one of up to n1/s labels is assigned to each node. A fixed stack process for routing packets on a tree, given a target stack depth, s, initially identifies a subset, S, of at nodes from the tree, such as at most 3 n1/s nodes, such that after the subset, S, is removed, each remaining subtree has at most n(s-1)/s nodes. A unique label is assigned to each of the nodes in the subset S and, within each remaining subtree, one of up to n(s-1)/s labels is assigned to each node. If the bound on the stack depth cannot be violated, the fixed stack routing process merges every two consecutive levels in the stack to one level.
    • 提供了一种方法和装置,用于在给定最大堆栈深度s的情况下路由布置在线或树(或前述的组合)中的多个n个节点内的分组。 给定堆栈深度s的线路上的路由数据包的固定堆栈过程最初将n个节点的一行划分成段,如n1 / s大致相等的段。 每个段分配唯一的标签,在每个段内,每个节点分配了多达n1 / s个标签之一。 给定目标堆栈深度s的用于在树上路由数据包的固定堆栈过程最初识别来自树的节点(例如最多3个n1 / s个节点)的子集S,使得在该子集之后,S 被删除,每个剩余的子树最多具有n(s-1)/ s个节点。 分配给子集S中的每个节点的唯一标签,并且在每个剩余子树中,每个节点分配多达n(s-1)/ s个标签之一。 如果不能违反堆栈深度的限制,则固定堆栈路由进程将堆栈中的每两个连续级别合并到一个级别。