{"_id":"18656","abstract":[{"lang":"eng","text":"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."}],"date_created":"2020-08-31T07:49:02Z","status":"public","department":[{"_id":"63"}],"user_id":"15415","page":"69-72","year":"2007","publication":"Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)","date_updated":"2022-01-06T06:53:50Z","type":"conference","language":[{"iso":"eng"}],"title":"StrSort Algorithms for Geometric Problems","citation":{"mla":"Sohler, Christian, and Christiane Lammersen. “StrSort Algorithms for Geometric Problems.” <i>Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)</i>, 2007, pp. 69–72.","ieee":"C. Sohler and C. Lammersen, “StrSort Algorithms for Geometric Problems,” in <i>Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)</i>, 2007, pp. 69–72.","ama":"Sohler C, Lammersen C. StrSort Algorithms for Geometric Problems. In: <i>Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)</i>. ; 2007:69-72.","apa":"Sohler, C., &#38; Lammersen, C. (2007). StrSort Algorithms for Geometric Problems. In <i>Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)</i> (pp. 69–72).","short":"C. Sohler, C. Lammersen, in: Proceedings of the 23rd European Workshop on Computational Geometry (EWCG), 2007, pp. 69–72.","chicago":"Sohler, Christian, and Christiane Lammersen. “StrSort Algorithms for Geometric Problems.” In <i>Proceedings of the 23rd European Workshop on Computational Geometry (EWCG)</i>, 69–72, 2007.","bibtex":"@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} }"},"author":[{"last_name":"Sohler","first_name":"Christian","full_name":"Sohler, Christian"},{"full_name":"Lammersen, Christiane","first_name":"Christiane","last_name":"Lammersen"}]}