Top-Down Skiplists

TL;DR

This paper introduces todolists, a novel variant of skiplists that achieves improved search comparison bounds and efficient updates, with experimental results showing competitive insertion times and superior search performance.

Contribution

We propose todolists, a new skiplist variant with better theoretical comparison bounds and practical efficiency, especially in search operations.

Findings

Todolists perform comparably to standard dictionaries in insertions.

Todolists outperform other structures in search times.

Achieves near-optimal comparison bounds for searches.

Abstract

We describe todolists (top-down skiplists), a variant of skiplists (Pugh 1990) that can execute searches using at most $\log_{2-\varepsilon} n + O(1)$ binary comparisons per search and that have amortized update time $O(\varepsilon^{-1}\log n)$. A variant of todolists, called working-todolists, can execute a search for any element $x$ using $\log_{2-\varepsilon} w(x) + o(\log w(x))$ binary comparisons and have amortized search time $O(\varepsilon^{-1}\log w(w))$. Here, $w(x)$ is the "working-set number" of $x$. No previous data structure is known to achieve a bound better than $4\log_2 w(x)$ comparisons. We show through experiments that, if implemented carefully, todolists are comparable to other common dictionary implementations in terms of insertion times and outperform them in terms of search times.