Computational complexity vs. runtime complexity: while the details are irrelevant for computational complexity, as you say, the runtime complexity is a differen

Computational complexity vs. runtime complexity: while the details are irrelevant for computational complexity, as you say, the runtime complexity is a different matter, because the execution environment (disk, cache, etc.) has been optimized to deliver better performance for certain types of operations. In the real world, it may thus be better to use a computationally more complex algorithm than a computationally simpler one in certain cases, if you happen to have a system that delivers big enough optimizations for the complex algorithm.