Computational geometry: an introduction
Computational geometry: an introduction
Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Balancing histogram optimality and practicality for query result size estimation
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Improved histograms for selectivity estimation of range predicates
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
The Aqua approximate query answering system
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Progressive vector transmission
Proceedings of the 7th ACM international symposium on Advances in geographic information systems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Wavelet synopses with error guarantees
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Locally adaptive dimensionality reduction for indexing large time series databases
ACM Transactions on Database Systems (TODS)
Access path selection in a relational database management system
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Optimal Histograms with Quality Guarantees
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Universality of Serial Histograms
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
The optimization of queries in relational databases
The optimization of queries in relational databases
Deterministic wavelet thresholding for maximum-error metrics
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximation and streaming algorithms for histogram construction problems
ACM Transactions on Database Systems (TODS)
REHIST: relative error histogram construction algorithms
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Fitting a Step Function to a Point Set
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Tight results for clustering and summarizing data streams
Proceedings of the 12th International Conference on Database Theory
Optimality and scalability in lattice histogram construction
Proceedings of the VLDB Endowment
Approximating Points by a Piecewise Linear Function: I
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximating Points by a Piecewise Linear Function: II. Dealing with Outliers
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Fitting a two-joint orthogonal chain to a point set
Computational Geometry: Theory and Applications
A randomized algorithm for weighted approximation of points by a step function
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Efficient construction of histograms for multidimensional data using quad-trees
Decision Support Systems
Representing a functional curve by curves with fewer peaks
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Outlier respecting points approximation
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
A deterministic algorithm for fitting a step function to a weighted point-set
Information Processing Letters
A note on searching line arrangements and applications
Information Processing Letters
| Hi-index | 0.00 |
Histograms and Wavelet synopses provide useful tools in query optimization and approximate query answering. Traditional histogram construction algorithms, e.g., V-Optimal, use error measures which are the sums of a suitable function, e.g., square, of the error at each point. Although the best-known algorithms for solving these problems run in quadratic time, a sequence of results have given us a linear time approximation scheme for these algorithms. In recent years, there have been many emerging applications where we are interested in measuring the maximum (absolute or relative) error at a point. We show that this problem is fundamentally different from the other traditional {\rm{non}}{\hbox{-}}\ell_\infty error measures and provide an optimal algorithm that runs in linear time for a small number of buckets. We also present results which work for arbitrary weighted maximum error measures.