The title is slightly misleading, I mean yes, naive binary search might have larger constant but the algorithm is still O(log(n)). This is still some "divide and conquer" style algorithm just with bunch of CPU specific optimizations. Also this works well with simple data structures, like integers, with more complex objects (custom comparators) it matters less.
The complexity of binary search in terms of "search" (comparison) operations is exactly log_2(n)+1, not just O(n). This algorithm just uses modern and current processor architecture artifacts to "improve" it on arrays of up to 4096 elements.
So not exactly "n" as in O(n).
Also: only for 16-bit integers.
> The complexity of binary search in terms of "search" (comparison) operations is exactly log_2(n)+1, not just O(n)
> So not exactly "n" as in O(n).
For large enough inputs the algorithm with better Big O complexity will eventually win (at least in the worst cases). Yes, sometimes it never happens in practice when the constants are too large. But say 100 * n * log(n) will eventually beat 5 * n for large enough n. Some advanced algorithms can use algorithms with worse Big O complexity but smaller constants for small enough sub-problems to improve performance. But it's more like to optimization detail rather than a completely different algorithm.
> This algorithm just uses modern and current processor architecture artifacts to "improve" it on arrays of up to 4096
Yes, that's my point. It's basically "I made binary search for integers X times faster on some specific CPUs". "Beating binary search" is somewhat misleading, it's more like "microptimizing binary search".
> The title is slightly misleading, I mean yes, naive binary search might have larger constant but the algorithm is still O(log(n)).
I think the title is not misleading since the Big O notation is only supposed to give a rough estimate of the performance of an algorithm.
(I agree though that binary search is already extremely fast, so making something twice as fast won't move the needle for the vast majority of applications where the speed bottleneck is elsewhere. Even infinite speed, i.e. instant sorted search, would likely not be noticeable for most software.)
For me it's slightly misleading because it's almost like saying "I wrote a faster quicksort implementation, so it beats quicksort!". In this case the binary search fundamental idea of "divide and conquer" is still there, the article just does microptimizations (which seem to be not very portable and are less relevant/applicible for more complex data structures) in order to reduce the constant part.
Yes, algorithmic complexity is theoretical, it often ignores the real world constants, but they are usually useful when comparing algorithms for larger inputs, unless we are talking about "galactic algorithms" with insanely large constants.