Hierarchical synopses with optimal error guarantees
ACM Transactions on Database Systems (TODS)
Tight results for clustering and summarizing data streams
Proceedings of the 12th International Conference on Database Theory
Unrestricted wavelet synopses under maximum error bound
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Multiplicative synopses for relative-error metrics
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
On Multidimensional Wavelet Synopses for Maximum Error Bounds
DASFAA '09 Proceedings of the 14th International Conference on Database Systems for Advanced Applications
Pseudo Period Detection on Time Series Stream with Scale Smoothing
APWeb/WAIM '09 Proceedings of the Joint International Conferences on Advances in Data and Web Management
Fast and effective histogram construction
Proceedings of the 18th ACM conference on Information and knowledge management
Optimality and scalability in lattice histogram construction
Proceedings of the VLDB Endowment
| Hi-index | 754.84 |
This paper addresses the problem of finding a B-term wavelet representation of a given discrete function fepsiRn whose distance from is minimized. The problem is well understood when we seek to minimize the Euclidean distance between f and its representation. The first-known algorithms for finding provably approximate representations minimizing general lp distances (including linfin) under a wide variety of compactly supported wavelet bases are presented in this paper. For the Haar basis, a polynomial time approximation scheme is demonstrated. These algorithms are applicable in the one-pass sublinear-space data stream model of computation. They generalize naturally to multiple dimensions and weighted norms. A universal representation that provides a provable approximation guarantee under all mu-norms simultaneously; and the first approximation algorithms for bit-budget versions of the problem, known as adaptive quantization, are also presented. Further, it is shown that the algorithms presented here can be used to select a basis from a tree-structured dictionary of bases and find a B-term representation of the given function that provably approximates its best dictionary-basis representation.