### Abstract

In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a given network, the above problems may or may not be solvable, depending on the amount of information about the attributes of the network made available to the processors. Some possibilities are: (1) no network attribute information at all is available, (2) an upper bound on the number of processors in the network is available, (3) the exact number of processors in the network is available, and (4) the topology of the network is available. In terms of a new graph property called symmetricity, in each of the four cases (1)-(4) above, we characterize the class of networks on which each of the four problems (a)-(d) is solvable. We then relate the symmetricity of a network to its 1- and 2-factors.

Original language | English |
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Pages (from-to) | 69-89 |

Number of pages | 21 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 1996 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*7*(1), 69-89. https://doi.org/10.1109/71.481599