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:
“Life is a thin narrowness of taken-for-granted, a plank over a canyon in a fog. There is something under our feet, the taken-for-granted. A table is a table, food is food, we are we—because we don’t question these things. And science is the enemy because it is the questioner. Faith saves our souls alive by giving us a universe of the taken-for-granted.”
—Rose Wilder Lane (1886–1968)
“This, our respectable daily life, on which the man of common sense, the Englishman of the world, stands so squarely, and on which our institutions are founded, is in fact the veriest illusion, and will vanish like the baseless fabric of a vision; but that faint glimmer of reality which sometimes illuminates the darkness of daylight for all men, reveals something more solid and enduring than adamant, which is in fact the cornerstone of the world.”
—Henry David Thoreau (1817–1862)
“From three to six months, most babies have settled down enough to be fun but aren’t mobile enough to be getting into trouble. This is the time to pay some attention to your relationship again. Otherwise, you may spend the entire postpartum year thinking you married the wrong person and overlooking the obvious—that parenthood can create rough spots even in the smoothest marriage.”
—Anne Cassidy (20th century)
“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)