Related to exponential in terms of? (nonetheless different from it):
Assume that you have an algorithm (producing gizmos) whose inputs are three numbers t, d, and h, which are interpreted by a human as the number of thingums, doodahs, and hickeys. Suppose the running time of the algorithm is the function g, which depends on t, d, and h. Further, let g(t,d,h) ≤ dᶜ, where c is some expression exceeding 1 and depending on t and h, but not on d.
I would like to use plain English to express this fact (e.g., in an abstract) in a simplified way. Do we write
The algorithm runs in polynomial time in the number of doodahs.
or
The algorithm runs in polynomial time with the number of doodahs.
?
My English teacher corrected it to
The algorithm runs in polynomial time in terms of the number of doodahs.
I think this cannot be quite right.
Which version is correct? And how about
The algorithm runs in worst-case polynomial time in/with the number of doodahs.
Any better version?
I welcome answers from mathematicians who are native AmE speakers and have an excellent command of English.
g(t,d,h) ≤ dᶜ
where c is a constant? Your time function doesn't appear to be bounded by a polynomial with a constant degree - since C is a function of other inputs to the algorithm. Or is the functionc(t, h)
bounded by a constant above? – Adam Jun 23 '17 at 23:08