### Abstract

In an "anonymous" network the processors have no identity numbers. We investigate the problem of computing a given function f on an asynchronous anonymous network in the sense that each processor computes f(I) for any input I = (I(ν_{1}),..., I(ν_{n})), where I(ν_{i}) is the input to processor ν_{i}, i = 1, 2,...,n. We address the following three questions: (1) What functions are computable on a given network? (2) Is there a "universal" algorithm which, given any network G and any function f computable on G as inputs, computes f on G? (3) How can one find lower bounds on the message complexity of computing various functions on anonymous networks? We give a necessary and sufficient condition for a function to be computable on an asynchronous anonymous network, and present a universal algorithm for computing f(I) on any network G, which accepts G and F computable on G, as well as {I(ν_{i})}, as inputs. The universal algorithm requires O(mn) messages in the worst case, where n and m are the numbers of processors and links in the network, respectively. We also propose a method for deriving a lower bound on the number of messages necessary to solve the above problem on asynchronous anonymous networks.

Original language | English |
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Pages (from-to) | 331-356 |

Number of pages | 26 |

Journal | Theory of Computing Systems |

Volume | 29 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Theory of Computing Systems*,

*29*(4), 331-356. https://doi.org/10.1007/BF01192691