Geodesic
Application of the method of sorting Schwartzian transform in the computational geometry
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 1 (2014), pp. 14-21.

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The article discusses the use of Schwartzian transform sorting applied to computational geometry objects. In computer science, the Schwartzian transform is a Perl programming idiom used to improve the efficiency of sorting a list of items. This idiom is appropriate for comparison-based sorting when the ordering is actually based on the ordering of a certain value of the elements of array, where computing this value is an intensive operation that should be performed a minimal number of times. The Schwartzian Transform for Perl language is notable in that it does not use named temporary arrays. We consider the question how to use Schwartzian transform for some computational geometry problems such that construct convex hull and orientation planar graph. The results is illustrated by tables with fulfilment time of sorting. The gain in time is approximately $3.3$ times. Also, we give implementation of Schwarzian transform for Python programming language.
Keywords: sorting, sorting methods, Schwartz transformation, sorting edges of graph, Perl and Python programming language. 
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V. A. Klyachin. Application of the method of sorting Schwartzian transform in the computational geometry. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 1 (2014), pp. 14-21. http://geodesic.mathdoc.fr/item/VVGUM_2014_1_a2/

[1] F. Preparata, M. Shamos, Computational Geometry: An Introduction, Mir Publ., M., 1985, 478 pp. | MR

[2] L. Wall, T. Christiansen, J. Orwant, Programming Perl, Simvol-plyus Publ., SPb., 2006, 1152 pp. | MR

[3] R.\;L. Schwartz, B.\;D. Foy, T. Phoenix, Intermediate Perl, Simvol-plyus Publ., SPb., 2007, 320 pp.

[4] Schwartzian transform, Electronic text data, , Title from screen http://en.wikipedia.org/wiki/Schwartzian_transform