Comparison Sort Lower Bound
The "Comparison Sort Lower Bound" refers to a theoretical limit on the efficiency of sorting algorithms that rely on comparing elements. It states that any comparison-based sorting algorithm must make at least Ω(n log n) comparisons in the worst case to sort n elements. This means that no matter how clever the algorithm is, it cannot sort a list of items faster than this bound when only using comparisons.
This lower bound is derived from the fact that there are n! possible arrangements of n elements, and each comparison can only eliminate half of these arrangements. Therefore, to determine the correct order, the algorithm must perform enough comparisons to narrow down the possibilities, leading to the Ω(n log n) requirement for efficiency in comparison sorts.