EPR-dictionaries: A practical and fast data structure for constant time searches in unidirectional and bidirectional FM-indices

TL;DR

This paper presents the EPR-dictionary, a new data structure enabling constant-time searches in FM-indices, significantly improving speed for bioinformatics applications like read mapping.

Contribution

The introduction of the EPR-dictionary replaces wavelet trees, achieving constant-time search steps in FM-indices with practical implementation and validation.

Findings

Achieved 2.6-4.8 times faster search in experiments.

First implementation of constant-time search in 2FM indices.

Validated theoretical efficiency with practical performance improvements.

Abstract

We introduce a new, practical method for conducting an exact search in a uni- and bidirectional FM index in $O(1)$ time per step while using $O(\log \sigma * n) + o(\log \sigma * \sigma * n)$ bits of space. This is done by replacing the binary wavelet tree by a new data structure, the Enhanced Prefixsum Rank dictionary (EPR-dictionary). We implemented this method in the SeqAn C++ library and experimentally validated our theoretical results. In addition we compared our implementation with other freely available implementations of bidirectional indices and show that we are between $\approx 2.6-4.8$ times faster. This will have a large impact for many bioinformatics applications that rely on practical implementations of (2)FM indices e.g. for read mapping. To our knowledge this is the first implementation of a constant time method for a search step in 2FM indices.