Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
A new algorithm for fitting a rectilinear x-monotone curve to a set of points in the plane
Pattern Recognition Letters
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Algorithms for optimal outlier removal
Journal of Discrete Algorithms
Weighted rectilinear approximation of points in the plane
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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
Outlier respecting points approximation
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A note on searching line arrangements and applications
Information Processing Letters
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We consider the problem of fitting a step function to a set of points. More precisely, given an integer kand a set Pof npoints in the plane, our goal is to find a step function fwith ksteps that minimizes the maximum vertical distance between fand all the points in P. We first give an optimal 茂戮驴(nlogn) algorithm for the general case. In the special case where the points in Pare given in sorted order according to their x-coordinates, we give an optimal 茂戮驴(n) time algorithm. Then, we show how to solve the weighted version of this problem in time O(nlog4n). Finally, we give an O(nh2logh) algorithm for the case where houtliers are allowed, and the input is sorted. The running time of all our algorithms is independent of k.