BACKGROUND Superbubbles are distinctive subgraphs in direct graphs that play an important role in assembly algorithms for high-throughput sequencing (HTS) data. Their practical importance derives from the fact they are connected to their host graph by a single entrance and a single exit vertex, thus allowing them to be handled independently. Efficient algorithms for the enumeration of superbubbles are therefore of important for the processing of HTS data. Superbubbles can be identified within the strongly connected components of the input digraph after transforming them into directed acyclic graphs. The algorithm by Sung et al. (IEEE ACM Trans Comput Biol Bioinform 12:770-777, 2015) achieves this task in O ( m l o g ( m ) ) -time. The extraction of superbubbles from the transformed components was later improved to by Brankovic et al. (Theor Comput Sci 609:374-383, 2016) resulting in an overall O ( m + n ) -time algorithm. RESULTS A re-analysis of the mathematical structure of superbubbles showed that the construction of auxiliary DAGs from the strongly connected components in the work of Sung et al. missed some details that can lead to the reporting of false positive superbubbles. We propose an alternative, even simpler auxiliary graph that solved the problem and retains the linear running time for general digraph. Furthermore, we describe a simpler, space-efficient O ( m + n ) -time algorithm for detecting superbubbles in DAGs that uses only simple data structures. IMPLEMENTATION We present a reference implementation of the algorithm that accepts many commonly used formats for the input graph and provides convenient access to the improved algorithm. https://github.com/Fabianexe/Superbubble.

中文翻译：

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重新审视超级泡沫。

背景技术超级气泡是直接图中的独特子图，在高通量测序（HTS）数据的组装算法中起着重要作用。它们的实际重要性源于它们通过单个入口和单个出口顶点连接到其宿主图的事实，从而允许独立处理它们。因此，用于枚举超级气泡的有效算法对于 HTS 数据的处理非常重要。在将输入有向图的强连通分量转换为有向无环图后，可以在它们中识别超级气泡。Sung 等人的算法。（IEEE ACM Trans Comput Biol Bioinform 12:770-777, 2015）在 O ( mlog ( m ) ) 时间内完成了这项任务。Brankovic 等人后来改进了从转化成分中提取超级气泡的方法。（Theor Comput Sci 609:374-383, 2016）导致整体 O ( m + n ) 时间算法。结果 对超级气泡数学结构的重新分析表明，在 Sung 等人的工作中，从强连通分量构建辅助 DAG。错过了一些可能导致误报超级气泡的细节。我们提出了一个替代的，甚至更简单的辅助图，它解决了这个问题并保留了一般有向图的线性运行时间。此外，我们描述了一种更简单、节省空间的 O ( m + n ) 时间算法，用于检测 DAG 中的超级气泡，该算法仅使用简单的数据结构。实现我们提出了一个算法的参考实现，它接受许多常用的输入图格式，并提供对改进算法的方便访问。https://github。