SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Reporting points in halfspaces
Computational Geometry: Theory and Applications
ACM Computing Surveys (CSUR)
The onion technique: indexing for linear optimization queries
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Efficient searching with linear constraints
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Optimal External Memory Interval Management
SIAM Journal on Computing
Evaluating top-k queries over web-accessible databases
ACM Transactions on Database Systems (TODS)
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Proceedings of the twenty-sixth annual symposium on Computational geometry
Tight lower bounds for halfspace range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
| Hi-index | 0.00 |
The ability to extract the most relevant information from a dataset is paramount when the dataset is large. For data arising from a numeric domain, a pervasive means of modelling the data is to represent it in the form of vectors. This enables a range of geometric techniques; this paper introduces projection as a natural and powerful means of scoring the relevancy of vectors. As yet, there are no effective indexing techniques for quickly retrieving those vectors in a dataset that have large projections onto a query vector. We address that gap by introducing the first indexing algorithms for vectors of arbitrary dimension, producing indices with strong sub-linear and output-sensitive worst-case query cost and linear data structure size guarantees in the I/O cost model. We improve this query cost markedly for the special case of two dimensions. The derivation of these algorithms results from the novel geometric insight that is presented in this paper, the concept of a data vector's cap.