The size of a genome graph -- the space required to store the nodes, their 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. The size of the graph also affects the size of the graph index that is used to speed up the alignment. This raises the need for approaches to construct space-efficient genome graphs.
We point out similarities in the string encoding approaches of genome graphs and the external pointer macro (EPM) compression model. Supported by these similarities, we present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. We show that the algorithms result in an upper bound on the size of the genome graph constructed based on an optimal EPM compression. In addition to the transformation, we show that equivalent choices made by EPM compression algorithms may result in different sizes of genome graphs. To further optimize the size of the genome graph, we purpose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel-Ziv EPM compression algorithm. We show that using RLZ-Graph, 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 de Bruijn graphs constructed by Bifrost under the default settings. The RLZ-Graph software is available at https://github.com/Kingsford-Group/rlzgraph