### Abstract

Let G = (X, Y, E) be a bipartite graph with integer weights on the edges. Let n, m, and N denote the vertex count, the edge count, and an upper bound on the absolute values of edge weights of G, respectively. For a vertex u in G, let G_{u} denote the graph formed by deleting u from G. The all-cavity maximum matching problem asks for a maximum weight matching in G_{u} for all u in G. This problem finds applications in optimal tree algorithms for computational biology. We show that the problem is solvable in. (formula presented) time, matching the currently best time complexity for merely computing a single maximum weight matching in G. We also give an algorithm for a generalization of the problem where both a vertex from X and one from Y can be deleted. The running time is (formula presented). Our algorithms are based on novel linear-time reductions among problems of computing shortest paths and all-cavity maximum matchings.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 8th International Symposium, ISAAC 1997, Proceedings |

Editors | Hon Wai Leong, Sanjay Jain, Hiroshi Imai |

Publisher | Springer Verlag |

Pages | 364-373 |

Number of pages | 10 |

ISBN (Print) | 3540638903, 9783540638902 |

DOIs | |

State | Published - Jan 1 1997 |

Event | 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 - Singapore, Singapore Duration: Dec 17 1997 → Dec 19 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1350 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 |
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Country | Singapore |

City | Singapore |

Period | 12/17/97 → 12/19/97 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Computation - 8th International Symposium, ISAAC 1997, Proceedings*(pp. 364-373). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1350). Springer Verlag. https://doi.org/10.1007/3-540-63890-3_39

}

*Algorithms and Computation - 8th International Symposium, ISAAC 1997, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1350, Springer Verlag, pp. 364-373, 8th Annual International Symposium on Algorithms and Computation, ISAAC 1997, Singapore, Singapore, 12/17/97. https://doi.org/10.1007/3-540-63890-3_39

**All-cavity maximum matchings.** / Kao, Ming Yang; Lam, Tak Wah; Sung, Wing Kin; Ting, Hing Fung.

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

TY - GEN

T1 - All-cavity maximum matchings

AU - Kao, Ming Yang

AU - Lam, Tak Wah

AU - Sung, Wing Kin

AU - Ting, Hing Fung

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Let G = (X, Y, E) be a bipartite graph with integer weights on the edges. Let n, m, and N denote the vertex count, the edge count, and an upper bound on the absolute values of edge weights of G, respectively. For a vertex u in G, let Gu denote the graph formed by deleting u from G. The all-cavity maximum matching problem asks for a maximum weight matching in Gu for all u in G. This problem finds applications in optimal tree algorithms for computational biology. We show that the problem is solvable in. (formula presented) time, matching the currently best time complexity for merely computing a single maximum weight matching in G. We also give an algorithm for a generalization of the problem where both a vertex from X and one from Y can be deleted. The running time is (formula presented). Our algorithms are based on novel linear-time reductions among problems of computing shortest paths and all-cavity maximum matchings.

AB - Let G = (X, Y, E) be a bipartite graph with integer weights on the edges. Let n, m, and N denote the vertex count, the edge count, and an upper bound on the absolute values of edge weights of G, respectively. For a vertex u in G, let Gu denote the graph formed by deleting u from G. The all-cavity maximum matching problem asks for a maximum weight matching in Gu for all u in G. This problem finds applications in optimal tree algorithms for computational biology. We show that the problem is solvable in. (formula presented) time, matching the currently best time complexity for merely computing a single maximum weight matching in G. We also give an algorithm for a generalization of the problem where both a vertex from X and one from Y can be deleted. The running time is (formula presented). Our algorithms are based on novel linear-time reductions among problems of computing shortest paths and all-cavity maximum matchings.

UR - http://www.scopus.com/inward/record.url?scp=84958045581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958045581&partnerID=8YFLogxK

U2 - 10.1007/3-540-63890-3_39

DO - 10.1007/3-540-63890-3_39

M3 - Conference contribution

AN - SCOPUS:84958045581

SN - 3540638903

SN - 9783540638902

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 364

EP - 373

BT - Algorithms and Computation - 8th International Symposium, ISAAC 1997, Proceedings

A2 - Leong, Hon Wai

A2 - Jain, Sanjay

A2 - Imai, Hiroshi

PB - Springer Verlag

ER -