Assertion: algorithm | /r/HasProperty | optimal
Facets:
value: asymptotically
type: MANNER
value: if
type: DEGREE
value: more formally
type: DEGREE
value: with respect to a particular resource
type: OTHER
value: in computer science
type: OTHER
Source sentences:
text: In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm.
text: More formally, an algorithm is asymptotically optimal with respect to a particular resource if the problem has been proven to require Ω(f(n)) of that resource, and the algorithm has been proven to use only O(f(n)).
text: A consequence of an algorithm being asymptotically optimal is that, for large enough inputs, no algorithm can outperform it by more than a constant factor.
text: Then, an algorithm which solves the problem in O(f(n)) time is said to be asymptotically optimal.
text: Then the algorithm is asymptotically optimal if:
text: Sometimes vague or implicit assumptions can make it unclear whether an algorithm is asymptotically optimal.
text: Whether this algorithm is asymptotically optimal is unknown, and would be likely to be hailed as a significant result if it were resolved either way.
text: At roughly the same time that Grover published his algorithm, Bennett, Bernstein, Brassard, and Vazirani proved that any quantum solution to the problem needs to evaluate the function Ω ( N ) {\displaystyle \Omega ({\sqrt {N}})} times, so Grover's algorithm is asymptotically optimal.
text: It is known that Grover's algorithm is optimal.