Median-of-k Jumplists and Dangling-Min BSTs

TL;DR

This paper enhances randomized jumplists by selecting jump pointers as medians of small samples, improving search efficiency and reducing memory use, and introduces a new analysis method via dangling-min BSTs.

Contribution

It extends jumplists with median-of-k jump pointers, maintains their distribution efficiently, and introduces dangling-min BSTs for analysis, addressing limitations of standard techniques.

Findings

Expected search, insert, delete costs are O(log n)

Omission of jump pointers in small sublists reduces memory without affecting search

Dangling-min BSTs provide a new analysis framework for jumplists

Abstract

We extend randomized jumplists introduced by Br\"onnimann et al. (STACS 2003) to choose jump-pointer targets as median of a small sample for better search costs, and present randomized algorithms with expected $O(\log n)$ time complexity that maintain the probability distribution of jump pointers upon insertions and deletions. We analyze the expected costs to search, insert and delete a random element, and we show that omitting jump pointers in small sublists hardly affects search costs, but significantly reduces the memory consumption. We use a bijection between jumplists and "dangling-min BSTs", a variant of (fringe-balanced) binary search trees for the analysis. Despite their similarities, some standard analysis techniques for search trees fail for dangling-min trees (and hence for jumplists).