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arXiv · 2004.06879

On the Complexity of the Plantinga-Vegter Algorithm

Felipe Cucker·Alperen A. Ergür·Josué Tonelli-Cueto
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Abstract

We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based algorithms in computational geometry. We combine these tools with the continuous amortization framework from exact computation. We use these tools on a well-known example from the subdivision family: the adaptive subdivision algorithm due to Plantinga and Vegter. The only existing complexity estimate on this rather fast algorithm was an exponential worst-case upper bound for its interval arithmetic version. We go beyond the worst-case by considering both average and smoothed analysis, and prove polynomial time complexity estimates for both interval arithmetic and finite-precision versions of the Plantinga-Vegter algorithm.

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Felipe Cucker, Alperen A. Ergür, Josué Tonelli-Cueto. 2020-04-15. On the Complexity of the Plantinga-Vegter Algorithm. https://doi.org/10.1007/s00454-022-00403-x

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