Computing Ultrabubbles in Linear Time by Reduction to Weak Superbubbles in the Double Covering Graph
Sebastian Schmidt, Juha Harviainen, Corentin Moumard, Aleksandr Politov, Francisco Sena, Alexandru I. Tomescu
In recent years, in attempts to capture variation structures in genomic and pangenomic graphs, the zoo of bubbles has been filled with more and more different variants. The first more complex variant was the superbubble which was later (informally) generalised to bidirected graphs as the ultrabubble. Ultrabubbles are more applicable in bioinformatics research, because genome and pangenome graphs usually are bidirected. In this paper, we study the relationship between superbubbles and ultrabubbles, and show that ultrabubbles in a bidirected graph are equivalent to the weak superbubbles in the corresponding double covering graph. Using this, we introduce a new linear-time algorithm to enumerate all ultrabubbles that consists of a very simple reduction to employ an existing linear-time algorithm to enumerate all weak superbubbles. Treating the superbubble algorithm as a black box, our algorithm is vastly simpler than the SPQR-tree-based linear-time ultrabubble enumeration algorithm of Sena et al. [2026]. Further, since our algorithm works on all bidirected graphs, it is strictly more powerful than the simple graph-orientation-based algorithm by Harviainen et al. [2026], which only works on a restricted class of bidirected graphs. In order to prove our equivalence, we additionally introduce simplified definitions of both ultrabubbles and weak superbubbles, through which the equivalence becomes more intuitive. Finally, our reduction motivates that some algorithmic problems in bidirected graphs can be reduced to well-known algorithmic problems in directed graphs.
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