## An improved algorithm for finding the strongly connected components of a directed graph (2005)

Citations: | 1 - 0 self |

### BibTeX

@TECHREPORT{Pearce05animproved,

author = {David J. Pearce},

title = {An improved algorithm for finding the strongly connected components of a directed graph},

institution = {},

year = {2005}

}

### OpenURL

### Abstract

For a directed graph D = (V,E), a Strongly Connected Component (SCC) is a maximal induced subgraph S = (VS,ES) where, for every x,y ∈ VS, there is a path from x to y (and vice-versa). Tarjan presented a now well-established algorithm for computing the strongly connected components of a digraph in time Θ(v+e) [8]. In the worst case, this needs v(2 + 5w) bits of storage, where w is the machine’s word size.

### Citations

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(Show Context)
Citation Context ... where, for every x,y ∈ VS, there is a path from x to y (and vice-versa). Tarjan presented a now well-established algorithm for computing the strongly connected components of a digraph in time Θ(v+e) =-=[8]-=-. In the worst case, this needs v(2 + 5w) bits of storage, where w is the machine’s word size. Nuutila and Soisalon-Soininen reduced this to v(1 + 4w) [6]. In this paper, we present for the first time... |

373 |
The SPIN Model Checker
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Citation Context ...is [1, 7] to name but a few. Of particular relevance is its use in model checking, where the algorithm’s storage requirements are a critical factor limiting the number of states which can be explored =-=[4]-=-. 2 Depth-First Search Algorithm 1 presents a well-known procedure for traversing digraphs, known as Depth First Search (DFS). We say that an edge v → w is traversed if visit(w) is called from visit(v... |

83 |
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(Show Context)
Citation Context ...e. Tarjan’s algorithm has found numerous uses in the literature, often as a subcomponent of larger algorithms, such as those for transitive closure [5], compiler optimisation [3] and program analysis =-=[1, 7]-=- to name but a few. Of particular relevance is its use in model checking, where the algorithm’s storage requirements are a critical factor limiting the number of states which can be explored [4]. 2 De... |

34 |
L.: “Transitive Closure Algorithms Based on Graph Traversal
- Ioannidis, Ramakrishnan, et al.
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(Show Context)
Citation Context ...n algorithm requiring only 3vw bits in the worst case. Tarjan’s algorithm has found numerous uses in the literature, often as a subcomponent of larger algorithms, such as those for transitive closure =-=[5]-=-, compiler optimisation [3] and program analysis [1, 7] to name but a few. Of particular relevance is its use in model checking, where the algorithm’s storage requirements are a critical factor limiti... |

30 | Path-based depth-first search for strong and biconnected components - Gabow - 2000 |

23 | On finding the strongly connected components in a directed graph
- Nuutila, Soisalon-soininen
- 1994
(Show Context)
Citation Context ...nected components of a digraph in time Θ(v+e) [8]. In the worst case, this needs v(2 + 5w) bits of storage, where w is the machine’s word size. Nuutila and Soisalon-Soininen reduced this to v(1 + 4w) =-=[6]-=-. In this paper, we present for the first time an algorithm requiring only 3vw bits in the worst case. Tarjan’s algorithm has found numerous uses in the literature, often as a subcomponent of larger a... |

7 |
Finding dominators revisited
- Georgiadis, Tarjan
- 2004
(Show Context)
Citation Context ...3vw bits in the worst case. Tarjan’s algorithm has found numerous uses in the literature, often as a subcomponent of larger algorithms, such as those for transitive closure [5], compiler optimisation =-=[3]-=- and program analysis [1, 7] to name but a few. Of particular relevance is its use in model checking, where the algorithm’s storage requirements are a critical factor limiting the number of states whi... |

3 | Efficient Field-Sensitive Pointer Analysis for C
- Pearce, Kelly, et al.
- 2004
(Show Context)
Citation Context ...e. Tarjan’s algorithm has found numerous uses in the literature, often as a subcomponent of larger algorithms, such as those for transitive closure [5], compiler optimisation [3] and program analysis =-=[1, 7]-=- to name but a few. Of particular relevance is its use in model checking, where the algorithm’s storage requirements are a critical factor limiting the number of states which can be explored [4]. 2 De... |