Predecessor problem on smooth distributions

TL;DR

This paper introduces a simplified approach to the predecessor problem on smooth distributions, extending the range of input types efficiently handled and providing insights into the performance of existing methods on smooth data.

Contribution

It proposes a simpler solution leveraging known results, broadening the class of distributions for efficient predecessor queries, and explaining why existing methods perform well on smooth inputs.

Findings

Extended the range of distributions with expected O(log log n) query time

Provided a simpler solution based on well-known results

Gained insights into the efficiency of related methods on smooth data

Abstract

We follow a research thread studying the predecessor problem on "smooth" distribution families. We propose a conceptually simpler solution utilizing well-known results from much better studied variant of the problem that assumes nothing about the input. As a side effect, we are able to extend the range of handled input distributions for the most studied case needing expected $\mathcal O(\log \log n)$ time, and we provide better insight into why the related methods are faster on smooth inputs.