Table of Common Time Complexities
Further information: Computational complexity of mathematical operationsThe following table summarises some classes of commonly encountered time complexities. In the table, poly(x) = xO(1), i.e., polynomial in x.
| Name | Complexity class | Running time (T(n)) | Examples of running times | Example algorithms |
|---|---|---|---|---|
| constant time | O(1) | 10 | Determining if an integer (represented in binary) is even or odd | |
| inverse Ackermann time | O(α(n)) | Amortized time per operation using a disjoint set | ||
| iterated logarithmic time | O(log* n) | Distributed coloring of cycles | ||
| log-logarithmic | O(log log n) | Amortized time per operation using a bounded priority queue | ||
| logarithmic time | DLOGTIME | O(log n) | log n, log(n2) | Binary search |
| polylogarithmic time | poly(log n) | (log n)2 | ||
| fractional power | O(nc) where 0 < c < 1 | n1/2, n2/3 | Searching in a kd-tree | |
| linear time | O(n) | n | Finding the smallest item in an unsorted array | |
| "n log star n" time | O(n log* n) | Seidel's polygon triangulation algorithm. | ||
| linearithmic time | O(n log n) | n log n, log n! | Fastest possible comparison sort | |
| quadratic time | O(n2) | n2 | Bubble sort; Insertion sort | |
| cubic time | O(n3) | n3 | Naive multiplication of two n×n matrices. Calculating partial correlation. | |
| polynomial time | P | 2O(log n) = poly(n) | n, n log n, n10 | Karmarkar's algorithm for linear programming; AKS primality test |
| quasi-polynomial time | QP | 2poly(log n) | nlog log n, nlog n | Best-known O(log2 n)-approximation algorithm for the directed Steiner tree problem. |
| sub-exponential time (first definition) |
SUBEXP | O(2nε) for all ε > 0 | O(2log nlog log n) | Assuming complexity theoretic conjectures, BPP is contained in SUBEXP. |
| sub-exponential time (second definition) |
2o(n) | 2n1/3 | Best-known algorithm for integer factorization and graph isomorphism | |
| exponential time | E | 2O(n) | 1.1n, 10n | Solving the traveling salesman problem using dynamic programming |
| factorial time | O(n!) | n! | Solving the traveling salesman problem via brute-force search | |
| exponential time | EXPTIME | 2poly(n) | 2n, 2n2 | |
| double exponential time | 2-EXPTIME | 22poly(n) | 22n | Deciding the truth of a given statement in Presburger arithmetic |
Read more about this topic: Time Complexity
Famous quotes containing the words table, common, time and/or complexities:
“When the painted birds laugh in the shade,
When our table with cherries and nuts is spread:
Come live, and be merry, and join with me
To sing the sweet chorus of ‘Ha, ha, he!’”
—William Blake (1757–1827)
“... a nation to be strong, must be united; to be united, must be equal in condition; to be equal in condition, must be similar in habits and feeling; to be similar in habits and feeling, must be raised in national institutions as the children of a common family, and citizens of a common country.”
—Frances Wright (1795–1852)
“You all talk like somebody else made these laws and Pharaoh don’t know nothing about ‘em. He makes ‘em his own self and he’s glad when we come tell him they hurt. why, that’s a whole lot of pleasure to him, to be making up laws all the time and to have a crowd like us around handy to pass all his mean ones on. Why, that’s a whole everything under the sun! Next thing you know he’ll be saying cats can’t have kittens.”
—Zora Neale Hurston (1891–1960)
“From infancy, a growing girl creates a tapestry of ever-deepening and ever- enlarging relationships, with her self at the center. . . . The feminine personality comes to define itself within relationship and connection, where growth includes greater and greater complexities of interaction.”
—Jeanne Elium (20th century)