### Abstract

We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. We do so constructively presenting two worst case optimal solution algorithms, one for anonymous systems, and one for those with distinct nodes ids.

Original language | English |
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Title of host publication | Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings |

Editors | Yingfei Dong, Ding-Zhu Du, Oscar Ibarra |

Place of Publication | Berlin; Heidelberg |

Publisher | Springer, Springer Nature |

Pages | 534-543 |

Number of pages | 10 |

Volume | 5878 LNCS |

ISBN (Electronic) | 9783642106316 |

ISBN (Print) | 3642106307, 9783642106309 |

DOIs | |

Publication status | Published - 2009 |

Event | 20th International Symposium on Algorithms and Computation, ISAAC - 2009 - Honolulu, United States Duration: 16 Dec 2009 → 18 Dec 2009 |

### 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 | 5878 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 20th International Symposium on Algorithms and Computation, ISAAC - 2009 |
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Country | United States |

City | Honolulu |

Period | 16/12/09 → 18/12/09 |

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## Cite this

*Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings*(Vol. 5878 LNCS, pp. 534-543). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS). Berlin; Heidelberg: Springer, Springer Nature. https://doi.org/10.1007/978-3-642-10631-6_55