The Complexity of the Hausdorff Distance

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The Complexity of the Hausdorff Distance
 
Jungeblut, Paul; Kleist, Linda; Miltzow, Till
(2022)
38th International Symposium on Computational Geometry, SoCG 2022, June 7-10, 2022, Berlin, Germany, volume 224, pp. 48:1 - 48:17
Leibniz International Proceedings in Informatics, LIPIcs, volume 224, pp. 48:1 - 48:17
(Part of book)
Abstract
We investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the Hausdorff distance of two semi-algebraic sets is bounded by a given threshold is complete for the complexity class ∀∃_
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Keywords: Hausdorff Distance, Semi-Algebraic Set, Existential Theory of the Reals, Universal Existential Theory of the Reals, Complexity Theory
DOI: https://doi.org/10.4230/LIPIcs.SoCG.2022.48
ISSN: 1868-8969
ISBN: 9783959772273
Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH
Note: Funding Information: Funding Linda Kleist: Partially supported by a postdoc fellowship of the German Academic Exchange Service (DAAD). Tillmann Miltzow: Generously supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 016.Veni.192.250. Publisher Copyright: © Paul Jungeblut, Linda Kleist, and Tillmann Miltzow; licensed under Creative Commons License CC-BY 4.0
(Peer reviewed)
 
 
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