Multidimensional indexing structure for use with linear optimization queries

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset

Processing Queries By Linear Constraints

The emergence of several new application domains for databases has introduced the need for more efficient complex query handling than databases currently support. These application domains include On-Line Analytical Processing (OLAP), Geographical Information Systems (GIS), and scientific databases. This paper focuses attention on a form of selection query, expressible in SQL but not evaluated efficiently by current DBMSs, with wide applicability in these new problem domains. We introduce a processing strategy for this class of queries, which we call queries by linear constraints (QBLC). This processing strategy can be implemented with a wide variety of multidimensional indexing structures that include the R-Tree variants, the k-d-B-Tree, the Buddy-Tree, and many more. Note that any processing strategy meant for general database use must guarantee that all correct answers are returned. Therefore, all numerical techniques we employ uphold this guarantee. Thus the most distinguishing ch..