Pairing Heaps with Costless Meld

TL;DR

This paper introduces a variation of pairing heaps that achieves zero amortized cost for meld operations while maintaining optimal bounds for other operations, simplifying the data structure and matching theoretical lower bounds.

Contribution

The paper presents a new pairing heap variant with costless meld operations and simplified structure, improving upon previous bounds and analysis.

Findings

Meld operation has zero amortized cost.

Other operations maintain optimal amortized bounds.

The new structure is simpler than previous variants.

Abstract

Improving the structure and analysis in \cite{elm0}, we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an $O(\log \log{n})$ in \cite{elm0}) and the same amortized bounds for all other operations. More precisely, the new pairing heap requires: no cost per meld, O(1) per find-min and insert, $O(\log{n})$ per delete-min, and $O(\log\log{n})$ per decrease-key. These bounds are the best known for any self-adjusting heap, and match the lower bound proved by Fredman for a family of such heaps. Moreover, the changes we have done make our structure even simpler than that in \cite{elm0}.