Space efficient merging of de Bruijn graphs and Wheeler graphs

TL;DR

This paper introduces a space-efficient algorithm for merging succinct de Bruijn graphs and explores the more complex problem of merging Wheeler graphs, including a novel approach for variable order representations.

Contribution

It presents a new, less space-consuming merging algorithm for de Bruijn graphs and offers the first space-efficient method for checking Wheeler graph union properties.

Findings

The new algorithm uses less than half the working space of existing methods.

It can compute variable order succinct representations within the same asymptotic bounds.

Wheeler graph merging is generally more complex, with a new algorithm for related decision problems.

Abstract

The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs. Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A novel important feature of our algorithm, not found in any of the existing tools, is that it can compute the Variable Order succinct representation of the union graph within the same asymptotic time/space bounds. In the second part of the paper we consider the more general problem of merging succinct representations of Wheeler graphs, a recently introduced graph family which includes as special cases de Bruijn graphs and many other known succinct indexes based on the BWT or one of its variants. We show that Wheeler graphs merging is in general a much more difficult problem, and we provide a space efficient algorithm for the slightly simplified problem of determining whether the union graph has an ordering that satisfies the Wheeler conditions.