Assertion: algorithm's time | /r/HasProperty | polynomial
Facets:
value: weakly
type: DEGREE
value: strongly
type: DEGREE
Source sentences:
text: Then it can be easily checked that the expected running time of A is polynomial but the expected running time of B is exponential.
text: These point sets do not seem to arise in practice: this is corroborated by the fact that the smoothed running time of k-means is polynomial.
text: 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 positive constant k. Problems for which a deterministic polynomial time algorithm exists belong to the complexity class P, which is central in the field of computational complexity theory.
text: The algorithm runs in strongly polynomial time if
text: An algorithm that runs in polynomial time but that is not strongly polynomial is said to run in weakly polynomial time.
text: An algorithm that runs in polynomial time but that is not strongly polynomial is said to run in weakly polynomial time.
text: (For example, a change from a single-tape Turing machine to a multi-tape machine can lead to a quadratic speedup, but any algorithm that runs in polynomial time under one model also does so on the other.)
text: An algorithm that solves a problem in nondeterministic polynomial time can run in polynomial time or exponential time depending on the choices it makes during execution.
text: For instance, in computational complexity, it is unknown whether P = BPP, i.e., we do not know whether we can take an arbitrary randomized algorithm that runs in polynomial time with a small error probability and derandomize it to run in polynomial time without using randomness.