Time Complexity - Polynomial Time

An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, i.e., T(n) = O(nk) for some constant k. Problems for which a polynomial time algorithm exists belong to the complexity class P, which is central in the field of computational complexity theory. Cobham's thesis states that polynomial time is a synonym for "tractable", "feasible", "efficient", or "fast".

Some examples of polynomial time algorithms:

  • The quicksort sorting algorithm on n integers performs at most operations for some constant A. Thus it runs in time and is a polynomial time algorithm.
  • All the basic arithmetic operations (addition, subtraction, multiplication, division, and comparison) can be done in polynomial time.
  • Maximum matchings in graphs can be found in polynomial time.

Read more about this topic:  Time Complexity

Famous quotes containing the word time:

    What is clear is that Christianity directed increased attention to childhood. For the first time in history it seemed important to decide what the moral status of children was. In the midst of this sometimes excessive concern, a new sympathy for children was promoted. Sometimes this meant criticizing adults. . . . So far as parents were put on the defensive in this way, the beginning of the Christian era marks a revolution in the child’s status.
    C. John Sommerville (20th century)