# A Flow Procedure for the Linearization of Genome Sequence Graphs

## Abstract

Efforts to incorporate human genetic variation into the reference human genome have converged on the idea of a graph representation of genetic variation within a species, a genome sequence graph. A sequence graph represents a set of individual haploid reference genomes as paths in a single graph. When that set of reference genomes is sufficiently diverse, the sequence graph implicitly contains all frequent human genetic variations, including translocations, inversions, deletions, and insertions.

In representing a set of genomes as a sequence graph one encounters certain challenges. One of the most important is the problem of graph linearization, essential both for efficiency of storage and access, as well as for natural graph visualization and compatibility with other tools. The goal of graph linearization is to order nodes of the graph in such a way that operations such as access, traversal and visualization are as efficient and effective as possible.

A new algorithm for the linearization of sequence graphs, called the flow procedure, is proposed in this paper. Comparative experimental evaluation of the flow procedure against other algorithms shows that it outperforms its rivals in the metrics most relevant to sequence graphs.

## Keywords

Sequence graph Linearization Flow procedure Feedback arcs Cut width Backbone Grooming## Notes

### Acknowledgements

We’d like to thank Erik Garrison and Glenn Hickey for helpful conversations. This work was supported by the National Human Genome Research Institute of the National Institutes of Health under Award Number 5U54HG007990 and grants from the W.M. Keck foundation and the Simons Foundation. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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