### Abstract

Original language | Undefined |
---|---|

Title of host publication | Proceedings of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013) |

Editors | C. Kaklamanis, K. Pruhs |

Place of Publication | Berlin, Germany |

Publisher | Springer |

Pages | 120-131 |

Number of pages | 12 |

ISBN (Print) | 978-3-319-08000-0 |

DOIs | |

Publication status | Published - 2014 |

Event | 11th Workshop on Approximation and Online Algorithms 2013 - Sophia Antipolis, France Duration: 5 Sep 2013 → 6 Sep 2013 http://algo2013.inria.fr/waoa.shtml |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Publisher | Springer International Publishing |

Volume | 8447 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th Workshop on Approximation and Online Algorithms 2013 |
---|---|

Abbreviated title | WAOA 2013 |

Country | France |

City | Sophia Antipolis |

Period | 5/09/13 → 6/09/13 |

Internet address |

### Keywords

- EWI-24832
- Graph factors
- METIS-305910
- Approximation algorithms
- IR-91426

### Cite this

*Proceedings of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013)*(pp. 120-131). (Lecture Notes in Computer Science; Vol. 8447). Berlin, Germany: Springer. https://doi.org/10.1007/978-3-319-08001-7_11

}

*Proceedings of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013).*Lecture Notes in Computer Science, vol. 8447, Springer, Berlin, Germany, pp. 120-131, 11th Workshop on Approximation and Online Algorithms 2013, Sophia Antipolis, France, 5/09/13. https://doi.org/10.1007/978-3-319-08001-7_11

**Approximability of Connected Factors.** / Cornelissen, Kamiel; Hoeksma, R.P.; Manthey, Bodo; Narayanaswamy, N.S.; Rahul, C.S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Approximability of Connected Factors

AU - Cornelissen, Kamiel

AU - Hoeksma, R.P.

AU - Manthey, Bodo

AU - Narayanaswamy, N.S.

AU - Rahul, C.S.

N1 - 10.1007/978-3-319-08001-7_11

PY - 2014

Y1 - 2014

N2 - Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte’s reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard – finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected d-factor. We give a 3-approximation for all d and improve this to an (r + 1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r + 1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.

AB - Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte’s reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard – finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected d-factor. We give a 3-approximation for all d and improve this to an (r + 1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r + 1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.

KW - EWI-24832

KW - Graph factors

KW - METIS-305910

KW - Approximation algorithms

KW - IR-91426

U2 - 10.1007/978-3-319-08001-7_11

DO - 10.1007/978-3-319-08001-7_11

M3 - Conference contribution

SN - 978-3-319-08000-0

T3 - Lecture Notes in Computer Science

SP - 120

EP - 131

BT - Proceedings of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013)

A2 - Kaklamanis, C.

A2 - Pruhs, K.

PB - Springer

CY - Berlin, Germany

ER -