On the efficiency of pairing heaps and related data structures

Abstract

The pairing heap is well regarded as an efficient data structure for implementing priority queue operations. It is included in the GNU C++ library. Strikingly simple in design, the pairing heap data structure nonetheless seems difficult to analyze, belonging to the genre of self-adjusting data structures. With its design originating as a self-adjusting analogue of the Fibonacci heap, it has been previously conjectured that the pairing heap provides constrant amortized time decrease-key operations, and experimental studies have supported this conjecture. This paper demonstrates, contrary to conjecture, that the pairing heap requires more than constant amortized time to perform decrease-key operations. Moreover, new experimental findings are presented that reveal detectable growth in the amortized cost of the decrease-key operation. Second, a unifying framework is developed that includes both pairing heaps and Fibonacci heaps. The parameter of interest in this framework is the storage capacity available in the nodes of the data structure for auxiliary balance information fields. In this respect Fibonacci heaps require log log n bits per node when n items are present. This is shown to be asymptotically optimal for data structures that achieve the same asymptotic performance bounds as Fibonacci heaps and fall within this framework.