Computational geometry: an introduction
Computational geometry: an introduction
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
A new algorithm for fitting a rectilinear x-monotone curve to a set of points in the plane
Pattern Recognition Letters
Approximating a set of points by a step function
Journal of Visual Communication and Image Representation
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
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
Weighted rectilinear approximation of points in the plane
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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
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The problem considered in this paper is: given an integer k 0 and a set P of n points in the plane each with a corresponding non-negative weight, find a step function f with k steps that minimize the maximum weighted vertical distance between f and all the points in P. We present a randomized algorithm to solve the problem in O(n log n) expected running time. The bound is obviously optimal for the unsorted input. The previously best known algorithm runs in O(n log2 n) worstcase time. Another merit of the algorithm is its simplicity. The algorithm is just a randomized implementation of Frederickson and Johnson's matrix searching technique, and it only exploits a simple data structure.