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arXiv · 2501.07707

Computational Geometry with Probabilistically Noisy Primitive Operations

David Eppstein·Michael T. Goodrich·Vinesh Sridhar
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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, dynamic 2D convex hulls, and Delaunay triangulations for noisy primitives in optimal time with high probability.

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David Eppstein, Michael T. Goodrich, Vinesh Sridhar. 2025-01-13. Computational Geometry with Probabilistically Noisy Primitive Operations. https://doi.org/10.4230/lipics.wads.2025.24

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