### 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) |
---|---|

Title of host publication | Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings |

Pages | 49-60 |

Number of pages | 12 |

DOIs | |

State | Published - Sep 20 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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

Country | Germany |

City | Saarbrucken |

Period | 9/5/11 → 9/9/11 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Approximating minimum manhattan networks in higher dimensions'. Together they form a unique fingerprint.

## Cite this

*Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings*(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