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File:Original Welzl's Algorithm Counter Example.png

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Summary

Description
Čeština: Algoritmus publikovaný roku 1991 nebránil zmenšování poloměru mezivýsledku.

Algoritmus publikovaný společně s Matouškem a Sharirem roku 1996 toto opravil. Implementace s MoveToFront heuristikou navržená v původním článku problém řešila implicitním nezmenšováním poloměru pro mezivýsledek posledních 4 bodů.

Na obrázku jsou chybně napsané poslední 3 černé číslice, protože algoritmus při třech zafixovaných bodech další body nevolí a rovnou vrací výsledek (ne nutně obsahující celou množinu).
English: Algorithm published in 1991 didn't prevent shrinking radius of subresult.

Algorithm published together with Matoušek and Sharir in 1996 corrected it. Implementation with MoveToFront heuristics suggested in the original paper solved the problem by implicit prevention of shrinking diameter for a subresult of the last 4 points.

There are wrongly written last 3 black numbers as the algorithm does not choose next points when there are 3 fixed points, and it returns result immediately (not necessary containing whole the set).
Date
Source Own work
Author Hippo.69

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Example of Welzl's algorithm run which returns wrong result

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2 March 2019

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current15:46, 2 March 2019Thumbnail for version as of 15:46, 2 March 2019597 × 561 (28 KB)Hippo.69User created page with UploadWizard

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