### Abstract

We consider minimum equivalent digraph problem, its maximum optimization variant and some non-trivial extensions of these two types of problems motivated by biological and social network applications. We provide -approximation algorithms for all the minimization problems and 2-approximation algorithms for all the maximization problems using appropriate primal-dual polytopes. We also show lower bounds on the integrality gap of the polytope to provide some intuition on the final limit of such approaches. Furthermore, we provide APX-hardness result for all those problems even if the length of all simple cycles is bounded by 5.

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

Title of host publication | Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings |

Pages | 74-85 |

Number of pages | 12 |

DOIs | |

State | Published - Sep 14 2009 |

Event | 11th International Symposium on Algorithms and Data Structures, WADS 2009 - Banff, AB, Canada Duration: Aug 21 2009 → Aug 23 2009 |

### Publication series

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

Volume | 5664 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th International Symposium on Algorithms and Data Structures, WADS 2009 |
---|---|

Country | Canada |

City | Banff, AB |

Period | 8/21/09 → 8/23/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings*(pp. 74-85). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5664 LNCS). https://doi.org/10.1007/978-3-642-03367-4_7

}

*Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5664 LNCS, pp. 74-85, 11th International Symposium on Algorithms and Data Structures, WADS 2009, Banff, AB, Canada, 8/21/09. https://doi.org/10.1007/978-3-642-03367-4_7

**Approximating transitive reductions for directed networks.** / Berman, Piotr; Dasgupta, Bhaskar; Karpinski, Marek.

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

TY - GEN

T1 - Approximating transitive reductions for directed networks

AU - Berman, Piotr

AU - Dasgupta, Bhaskar

AU - Karpinski, Marek

PY - 2009/9/14

Y1 - 2009/9/14

N2 - We consider minimum equivalent digraph problem, its maximum optimization variant and some non-trivial extensions of these two types of problems motivated by biological and social network applications. We provide -approximation algorithms for all the minimization problems and 2-approximation algorithms for all the maximization problems using appropriate primal-dual polytopes. We also show lower bounds on the integrality gap of the polytope to provide some intuition on the final limit of such approaches. Furthermore, we provide APX-hardness result for all those problems even if the length of all simple cycles is bounded by 5.

AB - We consider minimum equivalent digraph problem, its maximum optimization variant and some non-trivial extensions of these two types of problems motivated by biological and social network applications. We provide -approximation algorithms for all the minimization problems and 2-approximation algorithms for all the maximization problems using appropriate primal-dual polytopes. We also show lower bounds on the integrality gap of the polytope to provide some intuition on the final limit of such approaches. Furthermore, we provide APX-hardness result for all those problems even if the length of all simple cycles is bounded by 5.

UR - http://www.scopus.com/inward/record.url?scp=69949150660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69949150660&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03367-4_7

DO - 10.1007/978-3-642-03367-4_7

M3 - Conference contribution

AN - SCOPUS:69949150660

SN - 3642033660

SN - 9783642033667

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

SP - 74

EP - 85

BT - Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings

ER -