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:
“A man who can dominate a London dinner table can dominate the world. The future belongs to the dandy. It is the exquisites who are going to rule.”
—Oscar Wilde (1854–1900)
“Human life in common is only made possible when a majority comes together which is stronger than any separate individual and which remains united against all separate individuals. The power of this community is then set up as “right” in opposition to the power of the individual, which is condemned as “brute force.””
—Sigmund Freud (1856–1939)
“I was given the gifts of the artist, and the trouble that goes with them: So I have that blessing, and there was never a time that I questioned it or doubted it.... For forty years, I wanted to jump out of windows.”
—Louise Nevelson (1900–1988)
“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)