Heap building bounds

Abstract

We consider the lower bound for building a heap in the worst case and the upper bound in the average case. We will prove that the supposedly fastest algorithm in the average case [2] does not attain its claimed bound and indeed is slower than that in [6]. We will then prove that the adversarial argument for the claimed best lower bound in the worst case[1] is also incorrect and the adversarial argument used yields a bound which is worse than that in [5] given by an information theory argument. Finally, we have proven a lower bound of 1.37n + o(n) for building a heap in the worst case. © Springer-Verlag Berlin Heidelberg 2005.