### Abstract

D.R. Fulkerson [7] described a two-phase greedy algorithm to find a minimum cost spanning arborescence and to solve the dual linear program. This was extended by the present author for "kernel systems", a model including the rooted edge-connectivity augmentation problem, as well. A similar type of method was developed by D. Komblum [9] for "lattice polyhedra", a notion introduced by A. Hoffman and D.E. Schwanz [8]. In order to unify these approaches, here we describe a two-phase greedy algorithm working on a slight extension of lattice polyhedra. This framework includes the rooted node-connectivity augmentation problem, as well, and hence the resulting algorithm, when appropriately specialized, finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity by one. The only known algorithm for this problem used submodular flows. Actually, the specialized algorithm solves an extension of the rooted edge-connectivity and node-connectivity augmentation problem.

Original language | English |
---|---|

Pages (from-to) | 565-576 |

Number of pages | 12 |

Journal | Mathematical Programming, Series B |

Volume | 84 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research

### Cite this

**Increasing the rooted-connectivity of a digraph by one.** / Frank, A.

Research output: Contribution to journal › Article

*Mathematical Programming, Series B*, vol. 84, no. 3, pp. 565-576. https://doi.org/10.1007/s10107990073b

}

TY - JOUR

T1 - Increasing the rooted-connectivity of a digraph by one

AU - Frank, A.

PY - 1999

Y1 - 1999

N2 - D.R. Fulkerson [7] described a two-phase greedy algorithm to find a minimum cost spanning arborescence and to solve the dual linear program. This was extended by the present author for "kernel systems", a model including the rooted edge-connectivity augmentation problem, as well. A similar type of method was developed by D. Komblum [9] for "lattice polyhedra", a notion introduced by A. Hoffman and D.E. Schwanz [8]. In order to unify these approaches, here we describe a two-phase greedy algorithm working on a slight extension of lattice polyhedra. This framework includes the rooted node-connectivity augmentation problem, as well, and hence the resulting algorithm, when appropriately specialized, finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity by one. The only known algorithm for this problem used submodular flows. Actually, the specialized algorithm solves an extension of the rooted edge-connectivity and node-connectivity augmentation problem.

AB - D.R. Fulkerson [7] described a two-phase greedy algorithm to find a minimum cost spanning arborescence and to solve the dual linear program. This was extended by the present author for "kernel systems", a model including the rooted edge-connectivity augmentation problem, as well. A similar type of method was developed by D. Komblum [9] for "lattice polyhedra", a notion introduced by A. Hoffman and D.E. Schwanz [8]. In order to unify these approaches, here we describe a two-phase greedy algorithm working on a slight extension of lattice polyhedra. This framework includes the rooted node-connectivity augmentation problem, as well, and hence the resulting algorithm, when appropriately specialized, finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity by one. The only known algorithm for this problem used submodular flows. Actually, the specialized algorithm solves an extension of the rooted edge-connectivity and node-connectivity augmentation problem.

UR - http://www.scopus.com/inward/record.url?scp=0042156608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042156608&partnerID=8YFLogxK

U2 - 10.1007/s10107990073b

DO - 10.1007/s10107990073b

M3 - Article

VL - 84

SP - 565

EP - 576

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 3

ER -