### Abstract

We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ℝ^{d} , find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line segments whose total length is equal to the pair's Manhattan (that is, L _{1}-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless P=NP ). Approximation algorithms are known for 2D, but not for 3D. We present, for any fixed dimension d and any ε O, an O(n _{ε}-approximation. For 3D, we also give a 4(k-1)-approximation for the case that the terminals are contained in the union of κ≥2 parallel planes.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 49-60 |

Number of pages | 12 |

Volume | 6942 LNCS |

DOIs | |

State | Published - 2011 |

Event | 19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany Duration: Sep 5 2011 → Sep 9 2011 |

### Publication series

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

Volume | 6942 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 19th Annual European Symposium on Algorithms, ESA 2011 |
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Country | Germany |

City | Saarbrucken |

Period | 9/5/11 → 9/9/11 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 6942 LNCS, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS). https://doi.org/10.1007/978-3-642-23719-5_5

**Approximating minimum manhattan networks in higher dimensions.** / Das, Aparna; Gansner, Emden R.; Kaufmann, Michael; Kobourov, Stephen G; Spoerhase, Joachim; Wolff, Alexander.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 6942 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6942 LNCS, pp. 49-60, 19th Annual European Symposium on Algorithms, ESA 2011, Saarbrucken, Germany, 9/5/11. https://doi.org/10.1007/978-3-642-23719-5_5

}

TY - GEN

T1 - Approximating minimum manhattan networks in higher dimensions

AU - Das, Aparna

AU - Gansner, Emden R.

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Spoerhase, Joachim

AU - Wolff, Alexander

PY - 2011

Y1 - 2011

N2 - We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ℝd , find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line segments whose total length is equal to the pair's Manhattan (that is, L 1-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless P=NP ). Approximation algorithms are known for 2D, but not for 3D. We present, for any fixed dimension d and any ε O, an O(n ε-approximation. For 3D, we also give a 4(k-1)-approximation for the case that the terminals are contained in the union of κ≥2 parallel planes.

AB - We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ℝd , find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line segments whose total length is equal to the pair's Manhattan (that is, L 1-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless P=NP ). Approximation algorithms are known for 2D, but not for 3D. We present, for any fixed dimension d and any ε O, an O(n ε-approximation. For 3D, we also give a 4(k-1)-approximation for the case that the terminals are contained in the union of κ≥2 parallel planes.

UR - http://www.scopus.com/inward/record.url?scp=80052801807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052801807&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-23719-5_5

DO - 10.1007/978-3-642-23719-5_5

M3 - Conference contribution

SN - 9783642237188

VL - 6942 LNCS

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

SP - 49

EP - 60

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

ER -