### Abstract

This paper investigates the orientation problem on anonymous n×n torus networks. In the orientation problem, the goal is to reach an agreement, among all processors, on a consistent channel labelling. This paper shows that, if processors can label their channels arbitrarily, then there is no distributed orientation algorithm. Therefore the orientation problem is studied in various orientation models M that restrict local channel labellings. For many M, there are network labellings that, to the processors, are indistinguishable from orientations. These pseudo-orientations give rise to two problems related to orientation. In the verification problem, processors in an n×n torus distributively verify whether a network labelling in M is an orientation. The verification problem is shown to be equivalent to a problem of tiling the torus with Wang tiles. In the pseudo-orientation problem, the goal is to distributively find a pseudo-orientation. The pseudo-orientation problem is shown to be equivalent to a problem in graph theory.

Original language | English (US) |
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Title of host publication | Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings |

Editors | Andre Schipe |

Publisher | Springer Verlag |

Pages | 264-278 |

Number of pages | 15 |

ISBN (Print) | 9783540572718 |

State | Published - Jan 1 1993 |

Externally published | Yes |

Event | 7th International Workshop on Distributed Algorithms, WDAG 1993 - Lausanne, Switzerland Duration: Sep 27 1993 → Sep 29 1993 |

### 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 | 725 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Workshop on Distributed Algorithms, WDAG 1993 |
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Country | Switzerland |

City | Lausanne |

Period | 9/27/93 → 9/29/93 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings*(pp. 264-278). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 725 LNCS). Springer Verlag.