Computational Geometry with Probabilistically Noisy Primitives
2025-01-20
A new preprint explores computational geometry algorithms under probabilistically noisy primitive operations. Many such algorithms rely on primitives accessing input coordinates and converting them to combinatorial information. The paper considers primitives randomly producing incorrect results and investigates achieving high-probability correct outcomes without significant efficiency loss. It finds that for some problems (like convex hull construction), slowdown from repetition can be avoided, while for others (like finding closest pairs), it cannot. This connects to prior work on communication complexity using noisy comparisons to improve efficiency.
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