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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).
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]
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.
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 ...
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.
Identifying the in-place algorithms with L has some interesting implications; for example, it means that there is a (rather complex) in-place algorithm to determine whether a path exists between two nodes in an undirected graph, [3] a problem that requires O(n) extra space using typical algorithms such as depth-first search (a visited bit for ...
In other words, a problem with input size n is in NC if there exist constants c and k such that it can be solved in time O((log n) c) using O(n k) parallel processors. Stephen Cook [1] [2] coined the name "Nick's class" after Nick Pippenger, who had done extensive research [3] on circuits with polylogarithmic depth and polynomial size. [4]