Lucent Technologies Inc.

Sridhar Ramaswamy

Abraham Silberschatz

Viswanath Poosala

Swarup Acharya

Rajeev R Rastogi

Banu Rahime Ozden

Phillip B Gibbons

Kyuseok Shim

Torsten Suel

Sameer Mahajan

A method for generating an approximate answer to a query in a database environment in which the database has a plurality of base relations. A query relating to a database is received, and an approximate answer to the query is generated such that the approximate answer is based on at least one join synopsis formed from the database. The method further includes steps of forming a sample-tuple set for at least one selected base relation of a plurality of base relations of a database such that each sample-tuple set contains at least one sample tuple from a corresponding base relation, and forming a join synopsis set for each selected base relation such that each join synopsis set contains a join synopsis for each sample tuple in a sample-tuple set. A join synopsis of a sample tuple is based on a join of the sample tuple and at least one descendent relation of the sample tuple. All join synopsis sets form a statistical summary of the database and are stored.

Join synopsis-based approximate query answering

A new method for identifying a predetermined number of data points of interest in a large data set. The data points of interest are ranked in relation to the distance to their neighboring points. The method employs partition-based detection algorithms to partition the data points and then compute upper and lower bounds for each partition. These bounds are then used to eliminate those partitions that do contain the predetermined number of data points of interest. The data points of interest are then computed from the remaining partitions that were not eliminated. The present method eliminates a significant number of data points from consideration as the points of interest, thereby resulting in substantial savings in computational expense compared to conventional methods employed to identify such points.

Method for identifying outliers in large data sets

The present invention provides various methods and apparatus for providing accurate estimates for point and range queries over two-dimensional rectangular data. However, the techniques of the present invention for rectangular data can be applied to data of other shapes, point data, or linear data. The present invention provides several grouping techniques for the approximating of spatial data. A method is disclosed for grouping a plurality of spatial inputs into a plurality of buckets. In one form of the present invention the plurality of spatial inputs, is grouped based on an equi-area partitioning technique. The equi-area partitioning technique can use the longest dimension of a bucket or bounding polygon as the criteria for splitting into further buckets or bounding polygons. An equi-count technique can also be used wherein the buckets are split using the highest projected spatial input count along a dimension as a splitting criteria. The bounding polygons may be minimum bounding rectangles. In one form of the present invention a method is provided which uses a grid of regions superimposed over a plurality of spatial inputs. The method can determine a measure of the density of the spatial inputs within each region of the grid of regions and uses this measurement of density to determine how to group the spatial inputs into buckets. When a query is received the present invention applies the query to the buckets created by whatever method and gives an estimate of the number of spatial inputs contained within the query by preferably assuming that spatial inputs are uniformly distributed within each bucket.

Selectivity estimation in spatial databases

I/O-efficient methods and apparatus are provided for the d-dimensional join problem in one, two, and three dimensions, and are also generalized for arbitrary higher dimensions. Let N be the total number of rectangles in the two sets to be joined, M the total amount of memory available, B the disk block size, and T the total number of pairs in the output of the join. Define n&equals;N/B, m&equals;M/B, and t&equals;T/B. For one and two dimensions, I/O-optimal join methods are provided that run in O(nlog,n&plus;t) I/O operations and have utility to temporal and spatial database systems. For dimensions d&gE;3, methods are provided that run in O(nlog,n&plus;t) I/O operations, which is within a log,n factor of the currently known lower bounds.

System and method for performing I/O-efficient join processing

A system and method for discovering association rules that display regular cyclic variation over time is disclosed. Such association rules may apply over daily, weekly or monthly (or other) cycles of sales data or the like. A first technique, referred to as the sequential algorithm, treats association rules and cycles relatively independently. Based on the interaction between association rules and time, we employ a new technique called cycle pruning, which reduces the amount of time needed to find cyclic association rules. A second algorithm, the interleaved algorithm, uses cycle pruning and other optimization techniques for discovering cyclic association rules with reduced overhead.

Data mining using cyclic association rules

A system and method for determining calendric association rules are provided. The method uses calendars to describe the variation of association rules over time, where a specific calendar is defined as a collection of time intervals describing some phenomenon. In accordance with the invention, there is provided a method for identifying calendric association rules in transactional data with time stamped data items. In one exemplary embodiment, the method identifies large itemsets in each time unit, where a large itemset is an itemset that occurs in the transactions more than a given threshold. The method then identifies association rules of the form X&mdash;Y from the large itemsets by determining if a requisite support for the itemset XY and a given confidence threshold (ratio of (support of XY)/(support of X)) has been satisfied. Calendric association rules are then generated by examining identified association rules to determine which ones exhibit the temporal patterns specified by given calendars. In another embodiment, the method identifies large itemsets in each time unit, where an itemset includes at least one item type. The method then identifies calendars that belong to the large itemsets. Potential calendars for increasingly larger item type itemsets are generated by using previously identified calendars. Support values are calculated to determine which potential calendars actually belong to the itemsets and this is then used to determine what potential calendar association rules exist. The potential calendar association rule information and support values are used to determine which potential calendars actually belong to association rules.

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Scotch Plains, NJ, United States of America

Sridhar Ramaswamy