k-Violation linear programming
Information Processing Letters
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Efficient algorithms for mining outliers from large data sets
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
An on-line algorithm for fitting straight lines between data ranges
Communications of the ACM
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms for Mining Distance-Based Outliers in Large Datasets
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Note on Linear Time Algorithms for Maximum Error Histograms
IEEE Transactions on Knowledge and Data Engineering
Exploiting duality in summarization with deterministic guarantees
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
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
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
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In this paper, we consider a generalized problem formulation of computing a functional curve to approximate a point set in the plane with outliers. The goal is to seek a solution that not only optimizes its original objectives, but also somehow accommodates the impact of the outliers. Based on a new model of accommodating outliers, we present efficient geometric algorithms for various versions of this problem (e.g., the approximating functions are step functions or piecewise linear functions, the points are unweighted or weighted, etc). All our results are first known. Our new model and techniques for handling outliers may be useful to other applications as well.