Improved Upper Bounds for Pairing Heaps

Abstract

Pairing heaps are shown to have constant amortized time insert and zero amortized time meld, thus improving the previous O(log n) amortized time bound on these operations. It is also shown that pairing heaps have a distribution sensitive behavior whereby the cost to perform an extract-min on an element x is O(log min(n, k)) where k is the number of heap operations performed since x’s insertion. Fredman has observed that pairing heaps can be used to merge sorted lists of varying sized optimally, within constant factors. Utilizing the distribution sensitive behavior of pairing heap, an alternative method the employs pairing heaps for optimal list merging is derived.KeywordsActual CostPotential GainExecution SequenceWhite NodeBlack NodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.