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Abstract Motivation Intrasample heterogeneity describes the phenomenon where a genomic sample contains a diverse set of genomic sequences. In practice, the true string sets in a sample are often unknown due to limitations in sequencing technology. In order to compare heterogeneous samples, genome graphs can be used to represent such sets of strings. However, a genome graph is generally able to represent a string set universe that contains multiple sets of strings in addition to the true string set. This difference between genome graphs and string sets is not well characterized. As a result, a distance metric between genome graphs may not match the distance between true string sets.
Results We extend a genome graph distance metric, Graph Traversal Edit Distance (GTED) proposed by Ebrahimpour Boroojeny et al., to FGTED to model the distance between heterogeneous string sets and show that GTED and FGTED always underestimate the Earth Mover’s Edit Distance (EMED) between string sets. We introduce the notion of string set universe diameter of a genome graph. Using the diameter, we are able to upperbound the deviation of FGTED from EMED and to improve FGTED so that it reduces the average error in empirically estimating the similarity between true string sets. On simulated Tcell receptor sequences and actual Hepatitis B virus genomes, we show that the diametercorrected FGTED reduces the average deviation of the estimated distance from the true string set distances by more than 250%.
Availability and implementation Data and source code for reproducing the experiments are available at: https://github.com/KingsfordGroup/gtedemedtest/.
Supplementary information Supplementary data are available at Bioinformatics online.

Motivation: Intrasample heterogeneity describes the phenomenon where a genomic sample contains a diverse set of genomic sequences. In practice, the true string sets in a sample are often unknown due to limitations in sequencing technology. In order to compare heterogeneous samples, genome graphs can be used to represent such sets of strings. However, a genome graph is generally able to represent a string set universe that contains multiple sets of strings in addition to the true string set. This difference between genome graphs and string sets is not well characterized. As a result, a distance metric between genome graphs may not match the distance between true string sets. Results: We extend a genome graph distance metric, Graph Traversal Edit Distance (GTED) proposed by Ebrahimpour Boroojeny et al., to FGTED to model the distance between heterogeneous string sets and show that GTED and FGTED always underestimate the Earth Mover’s Edit Distance (EMED) between string sets. We introduce the notion of string set universe diameter of a genome graph. Using the diameter, we are able to upperbound the deviation of FGTED from EMED and to improve FGTED so that it reduces the average error in empirically estimating the similarity between true string sets. On simulated Tcell receptor sequences and actual Hepatitis B virus genomes, we show that the diametercorrected FGTED reduces the average deviation of the estimated distance from the true string set distances by more than 250%. Availability and implementation: Data and source code for reproducing the experiments are available at: https:// github.com/KingsfordGroup/gtedemedtest/.more » « less

Abstract Motivation The size of a genome graph—the space required to store the nodes, node labels and edges—affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. This raises the need for approaches to construct spaceefficient genome graphs.
Results We point out similarities in the string encoding mechanisms of genome graphs and the external pointer macro (EPM) compression model. We present a pair of lineartime algorithms that transform between genome graphs and EPMcompressed forms. The algorithms result in an upper bound on the size of the genome graph constructed in terms of an optimal EPM compression. To further reduce the size of the genome graph, we propose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proofofconcept, we introduce RLZGraph, a genome graph constructed based on the relative Lempel–Ziv algorithm. Using RLZGraph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored compacted de Bruijn graphs constructed by Bifrost under the default settings. The RLZGraph scales well in terms of running time and graph sizes with an increasing number of human genome sequences compared to Bifrost and variation graphs produced by VGtoolkit.
Availability The RLZGraph software is available at: https://github.com/KingsfordGroup/rlzgraph.
Supplementary information Supplementary data are available at Bioinformatics online.