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A Lower Bound for the Worst Case of Bottom-Up-Heapsort

Abstract Bottom-Up-Heapsort is a variant of Heapsort. Until now, its worst case complexity for the number of comparisons has been known to be bounded above by 1.5n log n + 0(n), where n is the number of elements to be sorted; but it was conjectured to be n log n + o(n log n). In this paper we give a construction that proves an asymptotic lower bound of 1.25n log n − 0(n log log n) comparisons for the worst case.