Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Sorting in c log n parallel steps
Combinatorica
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
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 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
Fitting a Step Function to a Point Set
Algorithmica - Special Issue: European Symposium on Algorithms
Efficient algorithms for the weighted k-center problem on a real line
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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Given a set of n points in the plane, each point having a positive weight, and an integer k0, we present an optimal O(nlogn)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance to the input points. It matches the expected time bound of the best known randomized algorithm for this problem. Our approach relies on Cole@?s improved parametric searching technique. As a direct application, our result yields the first O(nlogn)-time algorithm for computing a k-center of a set of n weighted points on the real line.