StrSort Algorithms for Geometric Problems

C. Sohler, C. Lammersen, in: Proceedings of the 23rd European Workshop on Computational Geometry (EWCG), 2007, pp. 69–72.

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In the StrSort model [2], the input is given as a stream, e.g. a sequence of points, and an algorithm can perform (a) streaming and (b) sorting passes to process the stream. A streaming pass reads the input stream from left to right and writes an output stream, which is the input of the next pass. A sorting pass is a black box operation that sorts a stream according to some partial order. In this paper, we develop algorithms for two basic geometric problems in the StrSort model. At first, we propose a divide-and-conquer algorithm that computes the convex hull of a point set in 2D in O(log2 n) passes using O(1) memory. Then we give a StrSort algorithm to compute a (1+ε)-spanner for a point set in Rd for constant d and constant epsilon that uses O(logd-1 n) passes and O(log n) space. This result implies a (1+ε)-approximation of the Euclidean minimum spanning tree in Rd, for constant d and ε.
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Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)
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69-72
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Sohler C, Lammersen C. StrSort Algorithms for Geometric Problems. In: Proceedings of the 23rd European Workshop on Computational Geometry (EWCG). ; 2007:69-72.
Sohler, C., & Lammersen, C. (2007). StrSort Algorithms for Geometric Problems. In Proceedings of the 23rd European Workshop on Computational Geometry (EWCG) (pp. 69–72).
@inproceedings{Sohler_Lammersen_2007, title={StrSort Algorithms for Geometric Problems}, booktitle={Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)}, author={Sohler, Christian and Lammersen, Christiane}, year={2007}, pages={69–72} }
Sohler, Christian, and Christiane Lammersen. “StrSort Algorithms for Geometric Problems.” In Proceedings of the 23rd European Workshop on Computational Geometry (EWCG), 69–72, 2007.
C. Sohler and C. Lammersen, “StrSort Algorithms for Geometric Problems,” in Proceedings of the 23rd European Workshop on Computational Geometry (EWCG), 2007, pp. 69–72.
Sohler, Christian, and Christiane Lammersen. “StrSort Algorithms for Geometric Problems.” Proceedings of the 23rd European Workshop on Computational Geometry (EWCG), 2007, pp. 69–72.

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