eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-14
24:1
24:13
10.4230/LIPIcs.ESA.2018.24
article
Improved Bounds for Multipass Pairing Heaps and Path-Balanced Binary Search Trees
Dorfman, Dani
1
Kaplan, Haim
1
Kozma, László
2
Pettie, Seth
3
Zwick, Uri
1
Blavatnik School of Computer Science, Tel Aviv University, Israel
Eindhoven University of Technology, The Netherlands
University of Michigan
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 * 2^{log^* n} * log^* n), respectively O(log n * 2^{log^* 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 Omega(log n).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol112-esa2018/LIPIcs.ESA.2018.24/LIPIcs.ESA.2018.24.pdf
data structure
priority queue
pairing heap
binary search tree