## Path-based depth-first search for strong and biconnected components (2000)

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Venue: | Information Processing Letters |

Citations: | 28 - 0 self |

### BibTeX

@ARTICLE{Gabow00path-baseddepth-first,

author = {Harold N. Gabow},

title = {Path-based depth-first search for strong and biconnected components},

journal = {Information Processing Letters},

year = {2000},

volume = {74},

pages = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

Key words: Graph, depth-first search, strongly connected component, biconnected component, stack.

### Citations

9061 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...in texts [1, 7, 14, 16, 17, 21]. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts =-=[2, 4, 6, 25]-=-. Tarjan's LOWPOINT biconnected component algorithm is presented in texts [1, 2, 4, 5, 7, 13, 14, 16, 17, 21, 25]. A twopass biconnected component algorithm of Micali that avoids LOWPOINT values is sk... |

2564 |
h~ Design and Analysis of Computer Algorithms
- Hopcroft, Ullman
- 1974
(Show Context)
Citation Context ...-first search. LOWPOINT values are regarded as crucial in the strong and biconnected component algorithms, e.g. [14, pp. 94, 514]. Tarjan's LOWPOINT method for strong components is presented in texts =-=[1, 7, 14, 16, 17, 21]-=-. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts [2, 4, 6, 25]. Tarjan's LOWPOIN... |

1259 |
Graph Theory
- Harary
- 1969
(Show Context)
Citation Context ...on is easily seen to be an equivalence relation over the edges, so the biconnected components are well-defined. The “blockcutpoint tree” of a graph represents the biconnected components and cutpoints =-=[12]-=-. We will use a hypergraph variant of this notion: The block hypergraph H of G is the hypergraph formed by merging the edges of each biconnected component of G. H is an acyclic hypergraph. In fact H c... |

1093 | Depth-first search and linear graph algorithms
- Tarjan
- 1972
(Show Context)
Citation Context ...rongly connected component, biconnected component, stack. 1 Introduction Depth-first search, as developed by Tarjan and co-authors, is a fundamental technique of efficient algorithm design for graphs =-=[23]-=-. This note presents depth-first search algorithms for two basic problems, strong and biconnected components. Previous algorithms either compute auxiliary quantities based on the depth-first search tr... |

771 |
Data Structures and Algorithms
- Aho, Hopcroft, et al.
- 1983
(Show Context)
Citation Context ...in texts [1, 7, 14, 16, 17, 21]. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts =-=[2, 4, 6, 25]-=-. Tarjan's LOWPOINT biconnected component algorithm is presented in texts [1, 2, 4, 5, 7, 13, 14, 16, 17, 21, 25]. A twopass biconnected component algorithm of Micali that avoids LOWPOINT values is sk... |

466 |
Algorithms
- Sedgewick
- 1998
(Show Context)
Citation Context ...-first search. LOWPOINT values are regarded as crucial in the strong and biconnected component algorithms, e.g. [14, pp. 94, 514]. Tarjan's LOWPOINT method for strong components is presented in texts =-=[1, 7, 14, 16, 17, 21]-=-. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts [2, 4, 6, 25]. Tarjan's LOWPOIN... |

267 | Efficiency of a good but not linear set union algorithm - Tarjan - 1975 |

238 | Efficient planarity testing
- Hopcroft, Tarjan
- 1974
(Show Context)
Citation Context ...intain a representation of the depth-first search path. This gives a simplified view of depth-first search without sacrificing efficiency. In greater detail, most depth-first search algorithms (e.g., =-=[23, 10, 11]-=-) compute so-called LOWPOINT values that are defined in terms of the depth-first search tree. Because of the success of this method LOWPOINT values have become almost synonymous with depth-first searc... |

185 |
Dividing a graph into triconnected components
- Hopcroft, Tarjan
- 1973
(Show Context)
Citation Context ...intain a representation of the depth-first search path. This gives a simplified view of depth-first search without sacrificing efficiency. In greater detail, most depth-first search algorithms (e.g., =-=[23, 10, 11]-=-) compute so-called LOWPOINT values that are defined in terms of the depth-first search tree. Because of the success of this method LOWPOINT values have become almost synonymous with depth-first searc... |

158 |
A linear-time algorithm for a special case of disjoint set union
- Gabow, Tarjan
- 1985
(Show Context)
Citation Context ... total time O(n2) and O(m + n log n) respectively. Tarjan has shown set merging can be more efficiently, giving total time O(mff(m; n) + n) [24]. In fact the incremental tree set merging algorithm of =-=[9]-=- can be used. This reduces the time to O(m + n), giving a linear time algorithm to find strong components. However the overhead of using incremental tree set merging may be significant in practice. Al... |

158 |
The Stanford GraphBase: A Platform for Combinatorial Computing
- Knuth
- 1993
(Show Context)
Citation Context ...-first search. LOWPOINT values are regarded as crucial in the strong and biconnected component algorithms, e.g. [14, pp. 94, 514]. Tarjan's LOWPOINT method for strong components is presented in texts =-=[1, 7, 14, 16, 17, 21]-=-. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts [2, 4, 6, 25]. Tarjan's LOWPOIN... |

157 |
Introduction to algorithms: A creative approach
- Manber
- 1989
(Show Context)
Citation Context ...first search. LOWPOINT values are regarded as crucial in the strong and biconnected component algorithms, e.g., [14, pp. 94, 514]. Tarjan’s LOWPOINT method for strong components is presented in texts =-=[1, 7,14,16,17,21]-=-. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptu1 Email: hal@cs.colorado.edu. ally simpler but it requires two passes over the graph. It is presented in texts [... |

117 |
Algorithmics: Theory and Practice
- Brassard, Bratley
- 1988
(Show Context)
Citation Context ...]. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptu1 Email: hal@cs.colorado.edu. ally simpler but it requires two passes over the graph. It is presented in texts =-=[2,4,6,25]-=-. Tarjan’s LOWPOINT biconnected component algorithm is presented in texts [1,2,4,5,7,13,14,16,17,21,25]. A two-pass biconnected component algorithm of Micali that avoids LOWPOINT values is sketched in... |

108 |
Data Structures and Algorithm Analysis
- Weiss
- 2006
(Show Context)
Citation Context ...in texts [1, 7, 14, 16, 17, 21]. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptually simpler but it requires two passes over the graph. It is presented in texts =-=[2, 4, 6, 25]-=-. Tarjan's LOWPOINT biconnected component algorithm is presented in texts [1, 2, 4, 5, 7, 13, 14, 16, 17, 21, 25]. A twopass biconnected component algorithm of Micali that avoids LOWPOINT values is sk... |

105 |
Hypergraphs: combinatorics of finite sets
- Berge
- 1989
(Show Context)
Citation Context ...S represent stack B. Arrows to the right of S represent the entries of I that are used in contract steps. E.g. in (a) the algorithm reads I[2] = 2 and then contracts cycle 2; 4; 5 to get (b). In (c) I=-=[3]-=- changes from 6 to 7, the latter being the strong component number of vertex 3. The algorithm consists of a main routine STRONG and a recursive procedure DFS: procedure STRONG(G) 1. empty stacks S and... |

104 |
Fundamentals of Algorithmics
- Brassard, Bratley
- 1996
(Show Context)
Citation Context ...ceptu1 Email: hal@cs.colorado.edu. ally simpler but it requires two passes over the graph. It is presented in texts [2,4,6,25]. Tarjan’s LOWPOINT biconnected component algorithm is presented in texts =-=[1,2,4,5,7,13,14,16,17,21,25]-=-. A two-pass biconnected component algorithm of Micali that avoids LOWPOINT values is sketched in [7, pp. 67–68]. This paper presents strong and biconnected component algorithms that are based on the ... |

86 |
Graph Algorithms, Computer Science
- Even
- 1979
(Show Context)
Citation Context |

43 |
Data Structures and Algorithms 2: Graph Algorithms and NP-Completeness
- Mehlhorn
- 1984
(Show Context)
Citation Context ...first search. LOWPOINT values are regarded as crucial in the strong and biconnected component algorithms, e.g., [14, pp. 94, 514]. Tarjan’s LOWPOINT method for strong components is presented in texts =-=[1, 7,14,16,17,21]-=-. The strong component algorithm of Kosaraju and Sharir [22] is often viewed as conceptu1 Email: hal@cs.colorado.edu. ally simpler but it requires two passes over the graph. It is presented in texts [... |

42 |
A theorem on graphs with an application to a problem on traffic control
- Robbins
- 1939
(Show Context)
Citation Context ...t-numbering [7], topological numbering, etc. The complete version of this paper [8] includes an algorithm to find the bridges of an undirected graph, leading to an immediate proof of Robbins' Theorem =-=[20]-=-. It also includes a simple articulation points algorithm, and a previously unpublished strong component algorithm of Tarjan that can be interpreted as path-based. Section 2 presents our strong compon... |

39 |
A strong-connectivity algorithm and its applications in data-flow analysis
- Sharir
- 1981
(Show Context)
Citation Context ...connected component algorithms, e.g., [14, pp. 94, 514]. Tarjan’s LOWPOINT method for strong components is presented in texts [1, 7,14,16,17,21]. The strong component algorithm of Kosaraju and Sharir =-=[22]-=- is often viewed as conceptu1 Email: hal@cs.colorado.edu. ally simpler but it requires two passes over the graph. It is presented in texts [2,4,6,25]. Tarjan’s LOWPOINT biconnected component algorithm... |

37 |
Combinatorial Problems and Exercises 2nd edition
- Lovasz
- 1993
(Show Context)
Citation Context ...ithms show that the simpler path-based view of depth-first search suffices for these properties. One can design other path-based depth-first search algorithms for properties such as ear decomposition =-=[15]-=-, st-numbering [7], topological numbering, etc. The complete version of this paper [8] includes an algorithm to find the bridges of an undirected graph, leading to an immediate proof of Robbins' Theor... |

19 |
A transitive closure algorithm
- Purdom
- 1970
(Show Context)
Citation Context ...hed in [7, pp.67-68]. This paper presents strong and biconnected component algorithms that are based on the depthfirst search path. This natural approach appears to have first been proposed by Purdom =-=[19]-=- and Munro [18] for strong components. It is regarded as requiring an extra data structure for set merging in order to be asymptotically efficient, and hence unlikely to be efficient in practice [23].... |

4 |
Efficient determination of the strongly connected components and the transitive closure of a graph.” Unpublished manuscript
- Munro
- 1971
(Show Context)
Citation Context ...7-68]. This paper presents strong and biconnected component algorithms that are based on the depthfirst search path. This natural approach appears to have first been proposed by Purdom [19] and Munro =-=[18]-=- for strong components. It is regarded as requiring an extra data structure for set merging in order to be asymptotically efficient, and hence unlikely to be efficient in practice [23]. We present lin... |

2 |
Data Structures and Algorithms 2: Graph Algorithms and NP-Completeness
- Melhorn
- 1984
(Show Context)
Citation Context |