Abstract: A technique for building probabilistic wavelet synopses for multi-measure data sets is provided. In the presence of multiple measures, it is demonstrated that the problem of exact probabilistic coefficient thresholding becomes significantly more complex. An algorithmic formulation for probabilistic multi-measure wavelet thresholding based on the idea of partial-order dynamic programming (PODP) is provided. A fast, greedy approximation algorithm for probabilistic multi-measure thresholding based on the idea of marginal error gains is provided. An empirical study with both synthetic and real-life data sets validated the approach, demonstrating that the algorithms outperform naive approaches based on optimizing individual measures independently and the greedy thresholding scheme provides near-optimal and, at the same time, fast and scalable solutions to the probabilistic wavelet synopsis construction problem.

Abstract: A grammar for mapping a first grouping of XML data into a second grouping of XML data and a method for accomplishing same to incorporate the first grouping into the second grouping. The grammar includes a first rule for computing a first child element attribute and a second rule for computing a second parent element attribute. The first rule and second rule vary according to a production of an element type of the first grouping. The element types include PCDATA, disjunctive, conjunctive and Kleene star, each having a unique rule set for defining inherited and synthesized attributes of the parent and child elements. The method includes the step of executing a mapping of a first grouping having at least one parent element and a set of corresponding child elements into a second grouping in accordance with the grammar rules based on the production of the element type.

Abstract: 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.

Abstract: Method for performing information-preserving DTD schema embeddings between a source schema when matching a source schema and a target schema. The preservation is realized by a matching process between the two schemas that finds a first string marking of the target schema, evaluates a legality of the first string marking, determines an estimated mimimal cost of the first string marking and subsequently adjusts the estimated minimal cost based upon one to one mapping of source schema and target schema subcomponents.

Abstract: A method of efficiently providing estimated answers to workloads of aggregate, multi-join SQL-like queries over a number of input data-streams. The method only examines each data elements once and uses a limited amount of computer memory. The method uses join graphs and atomic sketches that are essentially pseudo-random summaries formed using random binary variables. The estimated answer is the product of all the atomic sketches for all the vertices in the query join graph. A query workload is processed efficiently by identifying and sharing atomic sketches common to distinct queries, while ensuring that the join graphs remain well formed. The method may automatically minimize either the average query error or the maximum query error over the workload.

Abstract: A method and system for answering set-expression cardinality queries while lowering data communication costs by utilizing a coordinator site to provide global knowledge of the distribution of certain frequently occurring stream elements to significantly reduce the transmission of element state information to the central site and, optionally, capturing the semantics of the input set expression in a Boolean logic formula and using models of the formula to determine whether an element state change at a remote site can affect the set expression result.

Abstract: Method for providing controlled access to an XML document includes defining at least one access control policy for a user of the XML document, deriving a security view of the XML document for the user based upon said access control policy and schema level processing of the XML document and translating a user query based on the security view of the XML document to an equivalent query based on the XML document. An apparatus for same includes means for defining an access control policy for a user of the XML document and means for deriving a security view of the XML document for the user based on said access control policy and schema level processing of the XML document. Also included are means for translating a user query based on the security view of the XML document to an equivalent query based on the XML document.

Abstract: 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.

Abstract: A method of estimating an aggregate of a join over data-streams in real-time using skimmed sketches, that only examines each data element once and has a worst case space requirement of O(n2/J), where J is the size of the join and n is the number of data elements. The skimmed sketch is an atomic sketch, formed as the inner product of the data-stream frequency vector and a random binary variable, from which the frequency values that exceed a predetermined threshold have been skimmed off and placed in a dense frequency vector. The join size is estimated as the sum of the sub-joins of skimmed sketches and dense frequency vectors. The atomic sketches may be arranged in a hash structure so that processing a data element only requires updating a single sketch per hash table. This keeps the per-element overhead logarithmic in the domain and stream sizes.

Abstract: The invention provides methods and systems for summarizing multiple continuous update streams using corresponding multiple (parallel) JD Sketch data structures such that, for example, an approximate answer to a query requiring a join operation followed by a duplicate elimination step may be rapidly provided.

Abstract: 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.