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    • 8. 发明授权
    • Methods and apparatus for representing probabilistic data using a probabilistic histogram
    • 使用概率直方图表示概率数据的方法和装置
    • US08145669B2
    • 2012-03-27
    • US12636544
    • 2009-12-11
    • Graham CormodeAntonios DeligiannakisMinos GarofalakisAndrew Iain Shaw McGregor
    • Graham CormodeAntonios DeligiannakisMinos GarofalakisAndrew Iain Shaw McGregor
    • G06F7/00G06F17/30
    • G06F17/30536
    • Methods and apparatus for representing probabilistic data using a probabilistic histogram are disclosed. An example method comprises partitioning a plurality of ordered data items into a plurality of buckets, each of the data items capable of having a data value from a plurality of possible data values with a probability characterized by a respective individual probability distribution function (PDF), each bucket associated with a respective subset of the ordered data items bounded by a respective beginning data item and a respective ending data item, and determining a first representative PDF for a first bucket associated with a first subset of the ordered data items by partitioning the plurality of possible data values into a first plurality of representative data ranges and respective representative probabilities based on an error between the first representative PDF and a first plurality of individual PDFs characterizing the first subset of the ordered data items.
    • 公开了使用概率直方图表示概率数据的方法和装置。 一种示例性方法包括将多个有序数据项划分成多个桶,每个数据项能够具有来自多个可能数据值的数据值,其特征在于各自的概率分布函数(PDF), 每个桶与由相应的开始数据项和相应的结束数据项限定的有序数据项的相应子集相关联,并且通过分割多个数据项来确定与有序数据项的第一子集相关联的第一个桶的第一代表性PDF 基于第一代表性PDF和表征有序数据项的第一子集的第一多个单独PDF之间的误差,将可能的数据值转换成第一多个代表性数据范围和相应的代表概率。
    • 9. 发明授权
    • Streaming algorithms for robust, real-time detection of DDoS attacks
    • 用于强大,实时检测DDoS攻击的流式算法
    • US07669241B2
    • 2010-02-23
    • US10954901
    • 2004-09-30
    • Sumit GangulyMinos GarofalakisRajeev RastogiKrishan Sabnani
    • Sumit GangulyMinos GarofalakisRajeev RastogiKrishan Sabnani
    • G06F12/14
    • H04L29/06027H04L63/1458H04L65/607
    • A distinct-count estimate is obtained in a guaranteed small footprint using a two level hash, distinct count sketch. A first hash fills the first-level hash buckets with an exponentially decreasing number of data-elements. These are then uniformly hashed to an array of second-level-hash tables, and have an associated total-element counter and bit-location counters. These counters are used to identify singletons and so provide a distinct-sample and a distinct-count. An estimate of the total distinct-count is obtained by dividing by the distinct-count by the probability of mapping a data-element to that bucket. An estimate of the total distinct-source frequencies of destination address can be found in a similar fashion. By further associating the distinct-count sketch with a list of singletons, a total singleton count and a heap containing the destination addresses ordered by their distinct-source frequencies, a tracking distinct-count sketch may be formed that has considerably improved query time.
    • 使用两级散列,不同的计数草图在保证的小尺寸中获得不同的计数估计。 第一个散列填充了数据元素数量级数下降的第一级哈希桶。 然后将它们均匀地散列到二级哈希表的阵列,并具有关联的全元计数器和位位计数器。 这些计数器用于识别单例,因此提供了不同的样本和不同的数字。 通过将distinct-count除以将数据元素映射到该存储桶的概率,可以获得总区分计数的估计。 可以以类似的方式找到目的地地址的不同源频率的总体估计。 通过进一步将不同数量的草图与单例列表相关联,总共单例数和包含由其不同源频率排​​序的目的地地址的堆,可以形成具有显着改进的查询时间的跟踪不同计划草图。
    • 10. 发明授权
    • Tracking set-expression cardinalities over continuous update streams
    • 跟踪连续更新流中的设置表达式基数
    • US07596544B2
    • 2009-09-29
    • US11025355
    • 2004-12-29
    • Sumit GangulyMinos GarofalakisRajeev Rastogi
    • Sumit GangulyMinos GarofalakisRajeev Rastogi
    • G06F7/00
    • G06F17/30469Y10S707/99932
    • A method of estimating set-expression cardinalities over data streams with guaranteed small maintenance time per data-element update. The method only examines each data element once and uses a limited amount of memory. The time-efficient stream synopsis extends 2-level hash-sketches by randomly, but uniformly, pre-hashing data-elements prior to logarithmically hashing them to a first-level hash-table. This generates a set of independent 2-level hash-sketches. The set-union cardinality can be estimated by determining the smallest hash-bucket index j at which only a predetermined fraction of the b hash-buckets has a non-empty union |A∪B|. Once a set-union cardinality is estimated, general set-expression cardinalities may be estimated by counting witness elements for the set-expression, i.e., those first-level hash-buckets that are both a singleton for the set-expression and a set-union singleton. The set-expression cardinality is the set-union cardinality times the number of witness elements divided by the number of hash-buckets.
    • 一种估计数据流上的设置表达式基数的方法,每个数据元素更新保证小的维护时间。 该方法仅检查每个数据元素一次并使用有限的内存。 时间有效的流摘要通过随机,但统一地将数据元素进行对数散列之前的第一级散列表来扩展二级散列草图。 这产生一组独立的2级散列草图。 可以通过确定最小的哈希桶索引j来估计设置联合的基数,其中只有预定的b个哈希桶的一部分具有非空联合|A∪B|。 一旦估计了一个组合基数,就可以通过对集表达式的见证元素进行计数来估计一般的集合表示基数,即那些既是集合表达式的单例的一级哈希数据包, 联合单身人士 set-expression的基数是set-union的基数乘以证人的数量除以哈希桶的数量。