## Abstract

An efficient distributed algorithm is given for computing a single-source shortest path tree in an asynchronous planar network. The algorithm has message and time complexity O(pn) on an n-node network, where p is the smallest number of faces needed to cover all the nodes, taken over all possible plane embeddings of the network. The complexity of the algorithm ranges from O(n) to O(n^{2}) as p ranges from 1 to Θ(n). The algorithm incorporates optimal distributed solutions to a number of interesting subproblems inducting: (i) decomposing the plane embedding into Θ(p) outerplane graphs with favorable properties; (ii) a single-source algorithm for outerplane graphs; and (iii) identifying any edge in an outerplane graph whose cost exceeds the distance between its endpoints. As an application, an efficient message routing scheme is presented which adapts to changing link conditions and routes along near-shortest paths.

Original language | English (US) |
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Title of host publication | Distributed Algorithms - 4th International Workshop, Proceedings |

Editors | Jan van Leeuwen, Nicola Santoro |

Publisher | Springer Verlag |

Pages | 133-150 |

Number of pages | 18 |

ISBN (Print) | 9783540540991 |

DOIs | |

State | Published - 1991 |

Event | 4th International Workshop on Distributed Algorithms, WDAG 1990 - Bari, Italy Duration: Sep 24 1990 → Sep 26 1990 |

### 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 | 486 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th International Workshop on Distributed Algorithms, WDAG 1990 |
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Country/Territory | Italy |

City | Bari |

Period | 9/24/90 → 9/26/90 |

### Bibliographical note

Funding Information:1Research supported in part by a grant-in-aid of research from the Graduate School of the University of Minnesota. The first author was also supported in part by NSF grant CCR-8808574. Authors' e-mail addresses: janardan@umn-cs.cs.umn.edu; scheng~umn-cs.cs.umn.edu.

Publisher Copyright:

© 1991, Springer Verlag. All rights reserved.