Complexity theory’s 50-year journey to the limits of knowledge
This is an aside. But I twigged on a caption for one of the figures: “Every computational problem takes longer to solve as its input grows larger, but not all problems grow harder at the same rate.”It’s obvious from CS201 that this phrase is generally true and I have no pedantic objection to its inclusion in the article. However, I’m curious if this is strictly true or if we can find a (nontrivial) counterexample. Are there any algorithms that run faster as input grows? My first intuition is some kind of probabilistic question solved to a given correctness bound.Edit: it is trivial to construct an algorithm with this property. My precise question is whether any meaningful problems have optimal algorithms with this property.