### Abstract

This paper solves the problem of making a bipartite digraph strongly connected by adding the smallest number of new edges that preserve bipartiteness. A result of Baglivo and Graver shows this corresponds to making a 2-dimensional square grid framework with cables rigid by adding the smallest number of new cables. We prove a min-max formula for the smallest number of new edges in the digraph problem, and give a corresponding linear-time algorithm. We generalize these results to the problem of making an arbitrary digraph strongly connected by adding the smallest number of new edges, each of which joins vertices in distinct blocks of a given partition of the vertex set.

Original language | English |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Editors | Anon |

Publisher | SIAM |

Pages | 356-365 |

Number of pages | 10 |

Publication status | Published - 1999 |

Event | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA Duration: Jan 17 1999 → Jan 19 1999 |

### Other

Other | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | Baltimore, MD, USA |

Period | 1/17/99 → 1/19/99 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Discrete Mathematics and Combinatorics

### Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 356-365). SIAM.

**How to make a square grid framework with cables rigid.** / Gabow, Harold N.; Jordán, T.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.*SIAM, pp. 356-365, Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, 1/17/99.

}

TY - GEN

T1 - How to make a square grid framework with cables rigid

AU - Gabow, Harold N.

AU - Jordán, T.

PY - 1999

Y1 - 1999

N2 - This paper solves the problem of making a bipartite digraph strongly connected by adding the smallest number of new edges that preserve bipartiteness. A result of Baglivo and Graver shows this corresponds to making a 2-dimensional square grid framework with cables rigid by adding the smallest number of new cables. We prove a min-max formula for the smallest number of new edges in the digraph problem, and give a corresponding linear-time algorithm. We generalize these results to the problem of making an arbitrary digraph strongly connected by adding the smallest number of new edges, each of which joins vertices in distinct blocks of a given partition of the vertex set.

AB - This paper solves the problem of making a bipartite digraph strongly connected by adding the smallest number of new edges that preserve bipartiteness. A result of Baglivo and Graver shows this corresponds to making a 2-dimensional square grid framework with cables rigid by adding the smallest number of new cables. We prove a min-max formula for the smallest number of new edges in the digraph problem, and give a corresponding linear-time algorithm. We generalize these results to the problem of making an arbitrary digraph strongly connected by adding the smallest number of new edges, each of which joins vertices in distinct blocks of a given partition of the vertex set.

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M3 - Conference contribution

AN - SCOPUS:0032785087

SP - 356

EP - 365

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

A2 - Anon, null

PB - SIAM

ER -