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The worst-case complexity of the algorithm is dominated by the perfect matching step, which has () complexity. [2] Serdyukov's paper claimed O ( n 3 log n ) {\displaystyle O(n^{3}\log n)} complexity, [ 4 ] because the author was only aware of a less efficient perfect matching algorithm.
The first deterministic primality test significantly faster than the naive methods was the cyclotomy test; its runtime can be proven to be O((log n) c log log log n), where n is the number to test for primality and c is a constant independent of n. Many further improvements were made, but none could be proven to have polynomial running time.
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 ...
Using little omega notation, it is ω(n c) time for all constants c, where n is the input parameter, typically the number of bits in the input. For example, an algorithm that runs for 2 n steps on an input of size n requires superpolynomial time (more specifically, exponential time).
Cyclomatic complexity may also be applied to individual functions, modules, methods, or classes within a program. One testing strategy, called basis path testing by McCabe who first proposed it, is to test each linearly independent path through the program. In this case, the number of test cases will equal the cyclomatic complexity of the ...
DBSCAN executes exactly one such query for each point, and if an indexing structure is used that executes a neighborhood query in O(log n), an overall average runtime complexity of O(n log n) is obtained (if parameter ε is chosen in a meaningful way, i.e. such that on average only O(log n) points are returned).
The complexity of n is at most 3 log 2 n (approximately 4.755 log 3 n): an expression of this length for n can be found by applying Horner's method to the binary representation of n. [2] Almost all integers have a representation whose length is bounded by a logarithm with a smaller constant factor, 3.529 log 3 n. [3]
It is possible to find the maximum clique, or the clique number, of an arbitrary n-vertex graph in time O (3 n/3) = O (1.4422 n) by using one of the algorithms described above to list all maximal cliques in the graph and returning the largest one. However, for this variant of the clique problem better worst-case time bounds are possible.