Direct Superbubble Detection

Abstract

Superbubbles are a class of induced subgraphs in digraphs that play an essential role in assembly algorithms for high-throughput sequencing data. They are connected with the remainder of the host digraph by a single entrance and a single exit vertex. Linear-time algorithms for the enumeration superbubbles recently have become available. Current approaches require the decomposition of the input digraph into strongly-connected components, which are then analyzed separately. In principle, a single depth-first search could be used, provided one can guarantee that the root of the depth-first search (DFS)-tree is not itself located in the interior or the exit point of a superbubble. Here, we describe a linear-time algorithm to determine suitable roots for a DFS-forest that is guaranteed to identify the superbubbles in a digraph correctly. In addition to the advantages of a more straightforward implementation, we observe a nearly three-fold gain in performance on real-world datasets. We present a reference implementation of the new algorithm that accepts many commonly-used input formats for digraphs. It is available as open source from github.

Superbubbles as an empirical characteristic of directed networks

“…A key feature of superbubbles is that their vertices appear as an interval in the postorder of certain depth first search (DFS) trees (Brankovic et al, 2016;Gärtner et al, 2018b;Gärtner & Stadler, 2019). Although they may be nested, two superbubbles cannot have the same entrance or the same exit vertices (Onodera et al, 2013).…”

“…To detect superbubbles, we use the algorithm of Gärtner & Stadler (2019). First, it identifies a set of roots for DFSs.…”

“…In such cases, an auxiliary graph is analyzed in which an exit t is split into two, with one copy only retaining the incoming and the other retaining only the outgoing edges. We refer to Gärtner & Stadler (2019) for a detailed description of the algorithm.…”

“…Recall that superbubbles are computed with the help of a special DFS tree T. Note that several interesting quantities can be computed very efficiently. The reverse finishing order of a DFS equals the postorder of a DFS tree T (Gärtner & Stadler, 2019). In an acyclic graph, the postorder implies a topological sorting of the graph (Tarjan, 1972).…”

“…By definition, symmetric digraphs do not contain induced acyclic connected subgraphs with two or more vertices and thus do not contain superbubbles. Since all superbubbles in a digraph G can be identified and listed in linear time (Brankovic et al, 2016;Gärtner et al, 2018b;Gärtner & Stadler, 2019), they potentially serve as a genuine characteristic of directed features in G. The purpose of this contribution is to demonstrate empirically that superbubbles indeed provide useful quantitative parameters to describe digraphs.…”