Layered List Labeling

TL;DR

This paper introduces a novel data-structural approach that combines different list-labeling algorithms to achieve optimal bounds across worst-case, adaptive, and expected scenarios, resolving a long-standing tension in the field.

Contribution

The authors develop techniques to merge existing list-labeling solutions, enabling simultaneous optimal bounds in worst-case, adaptive, and expected settings.

Findings

Achieves combined bounds for list-labeling problems.

Resolves the tension between different bounds in list-labeling.

Provides a unified framework for multiple list-labeling algorithms.

Abstract

The list-labeling problem is one of the most basic and well-studied algorithmic primitives in data structures, with an extensive literature spanning upper bounds, lower bounds, and data management applications. The classical algorithm for this problem, dating back to 1981, has amortized cost $O(\log^2 n)$. Subsequent work has led to improvements in three directions: \emph{low-latency} (worst-case) bounds; \emph{high-throughput} (expected) bounds; and (adaptive) bounds for \emph{important workloads}. Perhaps surprisingly, these three directions of research have remained almost entirely disjoint -- this is because, so far, the techniques that allow for progress in one direction have forced worsening bounds in the others. Thus there would appear to be a tension between worst-case, adaptive, and expected bounds. List labeling has been proposed for use in databases at least as early as PODS'99, but a database needs good throughput, response time, and needs to adapt to common workloads (e.g., bulk loads), and no current list-labeling algorithm achieve good bounds for all three. We show that this tension is not fundamental. In fact, with the help of new data-structural techniques, one can actually \emph{combine} any three list-labeling solutions in order to cherry-pick the best worst-case, adaptive, and expected bounds from each of them.