On the Complexity of the Plantinga–Vegter Algorithm

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-...

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Vydané v:Discrete & computational geometry Ročník 68; číslo 3; s. 664 - 708
Hlavní autori: Cucker, Felipe, Ergür, Alperen A., Tonelli-Cueto, Josué
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.10.2022
Springer Nature B.V
Springer Verlag
Predmet:
Adaptive algorithms
Algorithms
Combinatorics
Complexity
Computational Geometry
Computational Mathematics and Numerical Analysis
Computer Science
Dimensional analysis
Estimates
Geometry
Interval arithmetic
Mathematics
Mathematics and Statistics
Numerical Analysis
Polynomials
Random variables
Upper bounds
Plantinga–Vegter algorithm
Subdivision methods
68W40
65D18
Complexity
Plantinga-Vegter algorithm
ISSN:0179-5376, 1432-0444
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-022-00403-x