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Computational Geometry with Probabilistically Noisy Primitive Operations

Authors David Eppstein, Michael T. Goodrich , Vinesh Sridhar

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Random walks and Markov chains
Keywords
  • Computational geometry
  • noisy comparisons
  • random walks

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Abstract

Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study computational geometry algorithms subject to noisy Boolean primitive operations in which, e.g., the comparison "is point q above line 𝓁?" returns the wrong answer with some fixed probability. We propose a novel technique called path-guided pushdown random walks that generalizes the results of noisy sorting. We apply this technique to solve point-location, plane-sweep, convex hulls in 2D and 3D, and Delaunay triangulations for noisy primitives in optimal time with high probability.

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David Eppstein, Michael T. Goodrich, and Vinesh Sridhar. Computational Geometry with Probabilistically Noisy Primitive Operations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.24

Author Details

David Eppstein
  • University of California, Irvine, CA, USA
Michael T. Goodrich
  • University of California, Irvine, CA, USA
Vinesh Sridhar
  • University of California, Irvine, CA, USA

Funding

  • Eppstein, David: Research supported in part by NSF grant CCF-2212129.
  • Goodrich, Michael T.: Research supported in part by NSF grant CCF-2212129.

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