The derivation of a tighter bound for top-down skew heaps

Abstract

In this paper we present and analyze functional programs for a number of priority queue operations. These programs are based upon the top-down 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 1.44 N log 2 N comparisons to sort N numbers (in the worst case).