### Abstract

A combinatorial algorithm for finding a feasible vector of the Edmonds-Giles polyhedron is presented. The algorithm is polynomially bounded provided that an oracle is available for minimizing submodular functions. A feasibility theorem is also proved by the algorithm and, as a consequence, a good algorithm for finding an integer-valued modular function between a sub- and a supermodular function is deduced. An important idea in the algorithm is due to Schönsleben and Lawler and Martel: the shortest augmenting paths have to be chosen in a lexicographic order.

Original language | English |
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Pages (from-to) | 221-239 |

Number of pages | 19 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1984 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Finding feasible vectors of Edmonds-Giles polyhedra.** / Frank, A.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 36, no. 3, pp. 221-239. https://doi.org/10.1016/0095-8956(84)90029-7

}

TY - JOUR

T1 - Finding feasible vectors of Edmonds-Giles polyhedra

AU - Frank, A.

PY - 1984

Y1 - 1984

N2 - A combinatorial algorithm for finding a feasible vector of the Edmonds-Giles polyhedron is presented. The algorithm is polynomially bounded provided that an oracle is available for minimizing submodular functions. A feasibility theorem is also proved by the algorithm and, as a consequence, a good algorithm for finding an integer-valued modular function between a sub- and a supermodular function is deduced. An important idea in the algorithm is due to Schönsleben and Lawler and Martel: the shortest augmenting paths have to be chosen in a lexicographic order.

AB - A combinatorial algorithm for finding a feasible vector of the Edmonds-Giles polyhedron is presented. The algorithm is polynomially bounded provided that an oracle is available for minimizing submodular functions. A feasibility theorem is also proved by the algorithm and, as a consequence, a good algorithm for finding an integer-valued modular function between a sub- and a supermodular function is deduced. An important idea in the algorithm is due to Schönsleben and Lawler and Martel: the shortest augmenting paths have to be chosen in a lexicographic order.

UR - http://www.scopus.com/inward/record.url?scp=0000100546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000100546&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(84)90029-7

DO - 10.1016/0095-8956(84)90029-7

M3 - Article

AN - SCOPUS:0000100546

VL - 36

SP - 221

EP - 239

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -