Ultrabubble enumeration via a lowest common ancestor approach

Athanasios E. Zisis; Pål Sætrom

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arXiv · 2603.03909

Ultrabubble enumeration via a lowest common ancestor approach

Athanasios E. Zisis·Pål Sætrom

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Abstract

Pangenomics uses graph-based models to represent and study the genetic variation between individuals of the same species or between different species. In such variation graphs, a path through the graph represents one individual genome. Subgraphs that encode locally distinct paths are therefore genomic regions with distinct genetic variation and detecting such subgraphs is integral for studying genetic variation. Biedged graphs is a type of variation graph that use two types of edges, black and grey, to represent genomic sequences and adjacencies between sequences, respectively. Ultrabubbles in biedged graphs are minimal subgraphs that represent a finite set of sequence variants that all start and end with two distinct sequences; that is, ultrabubbles are acyclic and all paths in an ultrabubble enter and exit through two distinct black edges. Ultrabubbles are therefore a special case of snarls, which are minimal subgraphs that are connected with two black edges to the rest of the graph. Here, we show that any bidirected graph can be transformed to a bipartite biedged graph in which lowest common ancestor queries can determine whether a snarl is an ultrabubble. This leads to an O(Kn) algorithm for finding all ultrabubbles in a set of K snarls, improving on the prior naive approach of O(K(n + m)) in a biedged graph with n nodes and m edges. Accordingly, our benchmark experiments on real and synthetic variation graphs show improved run times on graphs with few cycles and dead end paths, and dense graphs with many edges.

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Athanasios E. Zisis, Pål Sætrom. 2026-03-04. Ultrabubble enumeration via a lowest common ancestor approach. https://arxiv.org/abs/2603.03909

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