## Abstract

In this paper we study path layouts in communication networks. Stated in graph-theoretic terms, these layouts are translated into embeddings (or linear arrangements) of the vertices of a graph with N nodes onto the points 1, 2, N of the x-axis. We look for a graph with minimum diameter D^{L}_{c}(N), for which such an embedding is possible, given a bound c ou, the cutwidth of the embedding. We develop a technique to embed the nodes of such graphs into the integral lattice points in the c-dimensional li-sphere. Using this technique, we show that the minimum diameter D^{L}_{c}(N) satisfies Rc(N) ≤ D^{L}_{c}(N) ≤ 2Rc(N), where Rc(N) is the minimum radius of a c-dimensional li-sphere that conrains N points. Extensions of the results to augmented paths and ring networks are also presented. Using geometric arguments, we derive analytical bounds for Rc(N), which result in substantial improvements on some known lower and upper bounds.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 23rd International Workshop, WG 1997, Proceedings |

Editors | Rolf H. Mothring |

Publisher | Springer Verlag |

Pages | 171-183 |

Number of pages | 13 |

ISBN (Print) | 3540637575, 9783540637578 |

DOIs | |

State | Published - 1 Jan 1997 |

Externally published | Yes |

Event | 23rd International Workshop on Graph-Theoretic Concepts in Computer Science WG 1997 - Berlin, Germany Duration: 18 Jun 1997 → 20 Jun 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 | 1335 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd International Workshop on Graph-Theoretic Concepts in Computer Science WG 1997 |
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Country/Territory | Germany |

City | Berlin |

Period | 18/06/97 → 20/06/97 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)

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