An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Randomized optimal algorithm for slope selection
Information Processing Letters
Optimal slope selection via expanders
Information Processing Letters
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Asymptotically efficient in-place merging
Theoretical Computer Science
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
Algorithm Design
Space-efficient geometric divide-and-conquer algorithms
Computational Geometry: Theory and Applications
Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time
Computational Geometry: Theory and Applications
Line-segment intersection made in-place
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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Slope selection is a well-known algorithmic tool used in the context of computing robust estimators for fitting a line to a collection $\mathcal{P}$ of n points in the plane. We demonstrate that it is possible to perform slope selection in expected $\mathcal{O}{(n \log n)}$ time using only constant extra space in addition to the space needed for representing the input. Our solution is based upon a space-efficient variant of Matoušek's randomized interpolation search, and we believe that the techniques developed in this paper will prove helpful in the design of space-efficient randomized algorithms using samples. To underline this, we also sketch how to compute the repeated median line estimator in an in-place setting.