Are there any cases where you would prefer a higher big-O time complexity algorithm over the lower one?

Question

Are there are any cases where you would prefer O(log n) time complexity to O(1) time complexity? Or O(n) to O(log n)?

Answer 1

The possibility to execute an algorithm in parallel.

I don't know if there is an example for the classes O(log n) and O(1), but for some problems, you choose an algorithm with a higher complexity class when the algorithm is easier to execute in parallel.

Some algorithms cannot be parallelized but have so low complexity class. Consider another algorithm which achieves the same result and can be parallelized easily, but has a higher complexity class. When executed on one machine, the second algorithm is slower, but when executed on multiple machines, the real execution time gets lower and lower while the first algorithm cannot speed up.