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:
“I talk with the authority of failure—Ernest with the authority of success. We could never sit across the same table again.”
—F. Scott Fitzgerald (1896–1940)
“Throughout the 1980’s, we did hear too much about individual gain and the ethos of selfishness and greed. We did not hear enough about how to be a good member of a community, to define the common good and to repair the social contract. And we also found that while prosperity does not trickle down from the most powerful to the rest of us, all too often indifference and even intolerance do.”
—Hillary Rodham Clinton (b. 1947)
“Frequently also some fair-weather finery ripped off a vessel by a storm near the coast was nailed up against an outhouse. I saw fastened to a shed near the lighthouse a long new sign with the words “ANGLO SAXON” on it in large gilt letters, as if it were a useless part which the ship could afford to lose, or which the sailors had discharged at the same time with the pilot. But it interested somewhat as if it had been a part of the Argo, clipped off in passing through the Symplegades.”
—Henry David Thoreau (1817–1862)
“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)