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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.

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O (n + m) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O (m n · polylog (n)) time per update and requires only (3 m + o (m)) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions. [ABSTRACT FROM AUTHOR]