### Abstract

We devise a linear-time algorithm for finding an ambitus ín an undirected graph. An ambitus is a cycle in a graph containing two distinguished vertices such that certain different groups of bridges (called B^{ itp}-, B^{ itQ}-, and B^{ itPQ}-bridges) satisfy the property that a bridge in one group does not interlace with any bridge in the other groups. Thus, an ambitus allows the graph to be cut into pieces, where, in each piece, certain graph properties may be investigated independently and recursively, and then the pieces can be pasted together to yield information about these graph properties in the original graph. In order to achieve a good time-complexity for such an algorithm employing the divide-and-conquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, linear-time algorithms can be devised for abiding-path-finding and nonseparating-induced-cycle-finding problems.

Original language | English (US) |
---|---|

Pages (from-to) | 521-554 |

Number of pages | 34 |

Journal | Algorithmica (New York) |

Volume | 7 |

Issue number | 1-6 |

DOIs | |

State | Published - Jun 1992 |

### Fingerprint

### Keywords

- Abiding-path
- All-bidirectional-edges problem
- Ambitus
- Bridge
- Nonseparating induced cycle

### ASJC Scopus subject areas

- Applied Mathematics
- Safety, Risk, Reliability and Quality
- Software
- Computer Graphics and Computer-Aided Design

### Cite this

*Algorithmica (New York)*,

*7*(1-6), 521-554. https://doi.org/10.1007/BF01758776

**A linear-time algorithm for finding an ambitus.** / Mishra, Bhubaneswar; Tarjan, R. E.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 7, no. 1-6, pp. 521-554. https://doi.org/10.1007/BF01758776

}

TY - JOUR

T1 - A linear-time algorithm for finding an ambitus

AU - Mishra, Bhubaneswar

AU - Tarjan, R. E.

PY - 1992/6

Y1 - 1992/6

N2 - We devise a linear-time algorithm for finding an ambitus ín an undirected graph. An ambitus is a cycle in a graph containing two distinguished vertices such that certain different groups of bridges (called B itp-, B itQ-, and B itPQ-bridges) satisfy the property that a bridge in one group does not interlace with any bridge in the other groups. Thus, an ambitus allows the graph to be cut into pieces, where, in each piece, certain graph properties may be investigated independently and recursively, and then the pieces can be pasted together to yield information about these graph properties in the original graph. In order to achieve a good time-complexity for such an algorithm employing the divide-and-conquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, linear-time algorithms can be devised for abiding-path-finding and nonseparating-induced-cycle-finding problems.

AB - We devise a linear-time algorithm for finding an ambitus ín an undirected graph. An ambitus is a cycle in a graph containing two distinguished vertices such that certain different groups of bridges (called B itp-, B itQ-, and B itPQ-bridges) satisfy the property that a bridge in one group does not interlace with any bridge in the other groups. Thus, an ambitus allows the graph to be cut into pieces, where, in each piece, certain graph properties may be investigated independently and recursively, and then the pieces can be pasted together to yield information about these graph properties in the original graph. In order to achieve a good time-complexity for such an algorithm employing the divide-and-conquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, linear-time algorithms can be devised for abiding-path-finding and nonseparating-induced-cycle-finding problems.

KW - Abiding-path

KW - All-bidirectional-edges problem

KW - Ambitus

KW - Bridge

KW - Nonseparating induced cycle

UR - http://www.scopus.com/inward/record.url?scp=52449147018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449147018&partnerID=8YFLogxK

U2 - 10.1007/BF01758776

DO - 10.1007/BF01758776

M3 - Article

VL - 7

SP - 521

EP - 554

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1-6

ER -