Assertion: algorithm's time | /r/HasProperty | linear
Facets:
value: in the input lengths
type: OTHER
Source sentences:
text: However, for graphs that are sufficiently dense, Prim's algorithm can be made to run in linear time, meeting or improving the time bounds for other algorithms.
text: Various in-place merge algorithms have been devised, sometimes sacrificing the linear-time bound to produce an O(n log n) algorithm; see Merge sort § Variants for discussion.
text: For graphs of even greater density (having at least |V|c edges for some c > 1), Prim's algorithm can be made to run in linear time even more simply, by using a d-ary heap in place of a Fibonacci heap.
text: An algorithm is said to take linear time, or O(n) time, if its time complexity is O(n).
text: To find a single match of a single pattern, the expected time of the algorithm is linear in the combined length of the pattern and text, although its worst-case time complexity is the product of the two lengths.
text: To find multiple matches, the expected time is linear in the input lengths, plus the combined length of all the matches, which could be greater than linear.