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For example, the Adleman–Pomerance–Rumely primality test runs for n O(log log n) time on n-bit inputs; this grows faster than any polynomial for large enough n, but the input size must become impractically large before it cannot be dominated by a polynomial with small degree.
For example, in the search path for a string of length k, there will be k traversals down middle children in the tree, as well as a logarithmic number of traversals down left and right children in the tree. Thus, in a ternary search tree on a small number of very large strings the lengths of the strings can dominate the runtime.
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, M ( n ) {\displaystyle M(n)} below stands in for the complexity of the chosen multiplication algorithm.
Created independently in 1977 by W. Eddy and in 1978 by A. Bykat. Just like the quicksort algorithm, it has the expected time complexity of O(n log n), but may degenerate to O(n 2) in the worst case. Divide and conquer, a.k.a. merge hull — O(n log n) Another O(n log n) algorithm, published in 1977 by Preparata and Hong. This algorithm is also ...
The auxiliary indices have turned the search problem from a binary search requiring roughly log 2 N disk reads to one requiring only log b N disk reads where b is the blocking factor (the number of entries per block: b = 100 entries per block in our example; log 100 1,000,000 = 3 reads).
In computer science, polylogarithmic functions occur as the order of time for some data structure operations. Additionally, the exponential function of a polylogarithmic function produces a function with quasi-polynomial growth, and algorithms with this as their time complexity are said to take quasi-polynomial time. [2]
The iterated logarithm is useful in analysis of algorithms and computational complexity, appearing in the time and space complexity bounds of some algorithms such as: Finding the Delaunay triangulation of a set of points knowing the Euclidean minimum spanning tree: randomized O(n log * n) time. [3]
N-dimensional Quickhull was invented in 1996 by C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa. [1] It was an extension of Jonathan Scott Greenfield's 1990 planar Quickhull algorithm, although the 1996 authors did not know of his methods. [2] Instead, Barber et al. describe it as a deterministic variant of Clarkson and Shor's 1989 ...