Improved bounds for multipass pairing heaps and path-balanced binary search trees

Dani Dorfman, Haim Kaplan, László Kozma, Seth Pettie, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We revisit multipass pairing heaps and path-balanced binary search trees (BSTs), two classical algorithms for data structure maintenance. The pairing heap is a simple and efficient "self-adjusting" heap, introduced in 1986 by Fredman, Sedgewick, Sleator, and Tarjan. In the multipass variant (one of the original pairing heap variants described by Fredman et al.) the minimum item is extracted via repeated pairing rounds in which neighboring siblings are linked. Path-balanced BSTs, proposed by Sleator (cf. Subramanian, 1996), are a natural alternative to Splay trees (Sleator and Tarjan, 1983). In a path-balanced BST, whenever an item is accessed, the search path leading to that item is re-arranged into a balanced tree. Despite their simplicity, both algorithms turned out to be difficult to analyse. Fredman et al. showed that operations in multipass pairing heaps take amortized O(log n · log log n/log log log n) time. For searching in path-balanced BSTs, Balasubramanian and Raman showed in 1995 the same amortized time bound of O(log n · log log n/log log log n), using a different argument. In this paper we show an explicit connection between the two algorithms and improve both bounds to O(log n · 2log∗n · log n), respectively O (log n · 2log∗n · (log n)2), where log(·) denotes the slowly growing iterated logarithm function. These are the first improvements in more than three, resp. two decades, approaching the information-theoretic lower bound of Ω(log n).

Original languageEnglish
Title of host publication26th European Symposium on Algorithms, ESA 2018
EditorsHannah Bast, Grzegorz Herman, Yossi Azar
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770811
StatePublished - 1 Aug 2018
Event26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland
Duration: 20 Aug 201822 Aug 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference26th European Symposium on Algorithms, ESA 2018


FundersFunder number
National Science FoundationCCF-1637546, CCF-1514383
Seventh Framework Programme617951
European Research Council
United States-Israel Binational Science Foundation2012338
Israel Science Foundation1841-14
Tel Aviv University
Israeli Centers for Research Excellence4/11
National Science Foundation


    • Binary search tree
    • Data structure
    • Pairing heap
    • Priority queue


    Dive into the research topics of 'Improved bounds for multipass pairing heaps and path-balanced binary search trees'. Together they form a unique fingerprint.

    Cite this