The Derivation of a Tighter Bound for Top-Down Skew Heaps

In this paper we present and analyze functional programs for a number of priority queue operations. These programs are based upon the topdown skew heaps---a truly elegant data structure---designed by D.D. Sleator and R.E. Tarjan. We show how their potential technique can be used to determine the time complexity of functional programs. This functional approach enables us to derive a potential function leading to tighter bounds for the amortized costs of the priority queue operations. From the improved bounds it follows, for instance, that Skewsort, a simple sorting program using these operations, requires only about 1:44Nlog 2 N comparisons to sort N numbers (in the worst case). 1 Amortized complexity in a functional setting By means of a simple example we explain how the potential technique of Sleator and Tarjan [7] can be used to determine the time complexity of functional programs. In this example lists of zeros and ones are used as binary representations of natural numbers. We deno..