Introsort is a simple and effective algorithm which guarantes a sort as fast as Quicksort, but with Θ(N lg N ) worst case. It's well known that Quicksort has O(N lg N ) average complexity and O(N ^ 2) in worst case. This is true even for randomized variant of quicksort, or for the median of 3 pivoting strategy. Anyway, Quicksort is 2-5 time faster than Heapsort, which has Θ(N lg N) proven worst case.
In 1997, proposed to start with Quicksort and switch to Heapsort when the recursion depth is O(logN). This simple variant makes the Introsort algorithm Θ(N lg N ) worst case. Introsort is currently adopted as standard unstable sort by the Standard Template Library in stl_algo.h
"Introspective Sorting and Selection Algorithms". Software: Practice and Experience (Wiley) 27 (8): 983–993.