## Abstract

We address highly dynamic distributed systems

modeled by time-varying graphs (TVGs). We are interested in

proof of impossibility results that often use informal arguments

about convergence. First, we provide a topological distance metric

over sets of TVGs to correctly define the convergence of TVG

sequences in such sets. Next, we provide a general framework that

formally proves the convergence of the sequence of executions

of any deterministic algorithm over TVGs of any convergent

sequence of TVGs. Finally, we illustrate the relevance of the

above result by proving that no deterministic algorithm exists to

compute the underlying graph of any connected-over-time TVG,

i.e., any TVG of the weakest class of long-lived TVGs.

modeled by time-varying graphs (TVGs). We are interested in

proof of impossibility results that often use informal arguments

about convergence. First, we provide a topological distance metric

over sets of TVGs to correctly define the convergence of TVG

sequences in such sets. Next, we provide a general framework that

formally proves the convergence of the sequence of executions

of any deterministic algorithm over TVGs of any convergent

sequence of TVGs. Finally, we illustrate the relevance of the

above result by proving that no deterministic algorithm exists to

compute the underlying graph of any connected-over-time TVG,

i.e., any TVG of the weakest class of long-lived TVGs.

Original language | English |
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Title of host publication | IEEE International Symposium on Parallel & Distributed Processing, Workshops |

Publisher | IEEE Conference Publishing |

Pages | 0-0 |

Publication status | Published - 2015 |

Event | IEEE International Parallel & Distributed Processing Symposium - Hyderabad, India Duration: 25 May 2015 → 25 May 2015 |

### Conference

Conference | IEEE International Parallel & Distributed Processing Symposium |
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Country/Territory | India |

City | Hyderabad |

Period | 25/05/15 → 25/05/15 |

## Fields of Expertise

- Information, Communication & Computing

## Treatment code (Nähere Zuordnung)

- Theoretical