### Abstract

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 |
---|---|

Country | India |

City | Hyderabad |

Period | 25/05/15 → 25/05/15 |

### Fingerprint

### Fields of Expertise

- Information, Communication & Computing

### Treatment code (Nähere Zuordnung)

- Theoretical

### Cite this

*IEEE International Symposium on Parallel & Distributed Processing, Workshops*(pp. 0-0). IEEE Conference Publishing.

**A Generic Framework for Impossibility Results in Time-Varying Graphs.** / Braud-Santoni, Nicolas; Dubois, Swan; Kaaouachi, Mohamed-Hamza; Petit, Franck.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*IEEE International Symposium on Parallel & Distributed Processing, Workshops.*IEEE Conference Publishing, pp. 0-0, IEEE International Parallel & Distributed Processing Symposium, Hyderabad, India, 25/05/15.

}

TY - GEN

T1 - A Generic Framework for Impossibility Results in Time-Varying Graphs

AU - Braud-Santoni, Nicolas

AU - Dubois, Swan

AU - Kaaouachi, Mohamed-Hamza

AU - Petit, Franck

PY - 2015

Y1 - 2015

N2 - We address highly dynamic distributed systemsmodeled by time-varying graphs (TVGs). We are interested inproof of impossibility results that often use informal argumentsabout convergence. First, we provide a topological distance metricover sets of TVGs to correctly define the convergence of TVGsequences in such sets. Next, we provide a general framework thatformally proves the convergence of the sequence of executionsof any deterministic algorithm over TVGs of any convergentsequence of TVGs. Finally, we illustrate the relevance of theabove result by proving that no deterministic algorithm exists tocompute the underlying graph of any connected-over-time TVG,i.e., any TVG of the weakest class of long-lived TVGs.

AB - We address highly dynamic distributed systemsmodeled by time-varying graphs (TVGs). We are interested inproof of impossibility results that often use informal argumentsabout convergence. First, we provide a topological distance metricover sets of TVGs to correctly define the convergence of TVGsequences in such sets. Next, we provide a general framework thatformally proves the convergence of the sequence of executionsof any deterministic algorithm over TVGs of any convergentsequence of TVGs. Finally, we illustrate the relevance of theabove result by proving that no deterministic algorithm exists tocompute the underlying graph of any connected-over-time TVG,i.e., any TVG of the weakest class of long-lived TVGs.

M3 - Conference contribution

SP - 0

EP - 0

BT - IEEE International Symposium on Parallel & Distributed Processing, Workshops

PB - IEEE Conference Publishing

ER -