Efficient Bubble Enumeration in Directed Graphs

Birmelé, Étienne; Crescenzi, Pierluigi; Ferreira, Rui A. C.; Grossi, Roberto; Lacroix, Vincent; Marino, Andrea; Pisanti, Nadia; Sacomoto, Gustavo; Sagot, Marie‐France

doi:10.1007/978-3-642-34109-0_13

Cited by 15 publications

(19 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, by transforming each vertex v into an arc (v in , v out ), putting arcs (w out , v in ) and (v out , z in ) for each in-neighbor w and each out-neighbor z of v, vertex disjoint paths reduce to edge disjoint trails: as each of the k edge disjoint trails composing a solution do not use the same arc twice, we get the following. It is worth observing, that Theorem 3 generalizes the result in [1] for any k, getting the same bounds for k = 2, as O(F 2 (G)) is O(m).…”

Section: Vertex-disjoint Paths and Other Variationssupporting

confidence: 65%

“…Target not Given Target Given Target not Given k = 1 [7] and this paper (directed): O(m) [14]: O(nm) (directed) and O(m) (undirected) [2] (undirected): optimal this paper: O(m) k = 2 this paper: O(m) [1] and this paper: O(m) [11]: hard [15]: O(nm) this paper: O(m) k ≥ 3 this paper: O(m) [11]: hard [15]: hard Table 1. Cost per solution when listing the k vertex-disjoint (unbounded or bounded) paths originating from any given vertex s, whether the target t is given or not.…”

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 95%

“…st-paths of a directed or undirected graph [7], shortest st-paths [8], a special case of bounded length st-paths [14], bubbles, i.e. pairs of vertex-disjoint directed st-paths, of fixed length [1], bubbles starting from a given vertex s [15], k-disjoint shortest paths with k given pairs of sources and targets [3].…”

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 99%

“…For k > 1, it is related to graph connectivity (e.g. Menger's theorem [12] and its extensions) and the papers [1,3,8,14,15] in the above list present some variations. When k ordered pairs (s i , t i ) of vertices are specified, and s i t i -paths are sought for, the problem of finding these k disjoint paths is NP-hard for arbitrary k in undirected graph [9], and even for k = 2 in directed graphs [5].…”

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Algorithms for Listing k Disjoint st-Paths in Graphs

Grossi

Marino

Versari

2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Given a connected graph G of m edges and n vertices, we consider the basic problem of listing all the choices of k vertex-disjoint st-paths, for any two input vertices s, t of G and a positive integer k. Our algorithm takes O(m) time per solution, using O(m) space and requiring O(F k (G)) setup time, where F k (G) = O(m min{k, n 2/3 log n, √ m log n}) is the cost of running a max-flow algorithm on G to compute a flow of size k. The proposed techniques are simple and apply to other related listing problems discussed in the paper.

show abstract

Section: Vertex-disjoint Paths and Other Variationssupporting

confidence: 65%

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 95%

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 99%

Section: Unbounded Length Bounded Length Target Givenmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Algorithms for Listing k Disjoint st-Paths in Graphs

Grossi

Marino

Versari

2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the context of sequence analysis, a bubble can represent a potential sequencing error or a genetic variation within a set of homologous molecules. An efficient algorithm for bubble detection was proposed by [2].…”

Section: Introductionmentioning

confidence: 99%

Superbubbles, Ultrabubbles and Cacti

Paten¹,

Novak²,

Garrison

et al. 2017

Preprint

View full text Add to dashboard Cite

Abstract. A superbubble is a type of directed acyclic subgraph with single distinct source and sink vertices. In genome assembly and genetics, the possible paths through a superbubble can be considered to represent the set of possible sequences at a location in a genome. Bidirected and biedged graphs are a generalization of digraphs that are increasingly being used to more fully represent genome assembly and variation problems. Here we define snarls and ultrabubbles, generalizations of superbubbles for bidirected and biedged graphs, and give an efficient algorithm for the detection of these more general structures. Key to this algorithm is the cactus graph, which we show encodes the nested decomposition of a graph into snarls and ultrabubbles within its structure. We propose and demonstrate empirically that this decomposition on bidirected and biedged graphs solves a fundamental problem by defining genetic sites for any collection of genomic variations, including complex structural variations, without need for any single reference genome coordinate system. Furthermore, the nesting of the decomposition gives a natural way to describe and model variations contained within large variations, a case not currently dealt with by existing formats, e.g. VCF.

show abstract

A Family of Tree-Based Generators for Bubbles in Directed Graphs

Acuña

Lima

Italiano

et al. 2020

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Bubbles are pairs of internally vertex-disjoint (s, t)-paths in a directed graph. In de Bruijn graphs built from reads of RNA and DNA data, bubbles represent interesting biological events, such as alternative splicing (AS) and allelic differences (SNPs and indels). However, the set of all bubbles in a de Bruijn graph built from real data is usually too large to be efficiently enumerated and analysed in practice. In particular, despite significant research done in this area, listing bubbles still remains the main bottleneck for tools that detect AS events in a reference-free context. Recently, in [1] the concept of a bubble generator was introduced as a way for obtaining a compact representation of the bubble space of a graph. Although this generator was quite effective in finding AS events, preliminary experiments showed that it is about 5 times slower than state-of-art methods.In this paper we propose a new family of bubble generators which improve substantially on the previous generator: generators in this new family are about two orders of magnitude faster and are still able to achieve similar precision in identifying AS events. To highlight the practical value of our new generators, we also report some experimental results on a real dataset.

show abstract

Efficient Bubble Enumeration in Directed Graphs

Cited by 15 publications

References 12 publications

Efficient Algorithms for Listing k Disjoint st-Paths in Graphs

Efficient Algorithms for Listing k Disjoint st-Paths in Graphs

Superbubbles, Ultrabubbles and Cacti

A Family of Tree-Based Generators for Bubbles in Directed Graphs

Contact Info

Product

Resources

About