What sort algorithm provides the best worst-case performance?

Question

What is the fastest known sort algorithm for absolute worst case? I don\'t care about best case and am assuming a gigantic data set if that even matters.

Answer 1

For the man with limitless budget

Facetious but correct: Sorting networks trade space (in real hardware terms) for better than O(n log n) sorting!

Without resorting to such hardware (which is unlikely to be available) you have a lower bound for the best comparison sorts of O(n log n)

O(n log n) worst case performance (no particular order)

• Binary Tree Sort
• Merge Sort
• Heap Sort
• Smooth Sort
• Intro Sort

Beating the n log n

If your data is amenable to it you can beat the n log n restriction but instead care about the number of bits in the input data as well

Radix and Bucket are probably the best known examples of this. Without more information about your particular requirements it is not fruitful to consider these in more depth.