### Abstract

We introduce temporal flows on temporal networks [17, 19], i.e., networks the links of which exist only at certain moments of time. Such networks are ephemeral in the sense that no link exists after some time. Our flow model is new and diﬀers from the “flows over time” model, also called “dynamic flows” in the literature. We show that the problem of finding the maximum amount of flow that can pass from a source vertex s to a sink vertex t up to a given time is solvable in Polynomial time, even when node buﬀers are bounded. We then examine mainly the case of unbounded node buﬀers. We provide a simplified static Time-Extended network (STEG), which is of polynomial size to the input and whose static flow rates are equivalent to the respective temporal flow of the temporal network; using STEG, we prove that the maximum tem-poral flow is equal to the minimum temporal s-t cut. We further show that temporal flows can always be decomposed into flows, each of which moves only through a journey, i.e., a directed path whose successive edges have strictly increasing moments of existence. We partially char-acterise networks with random edge availabilities that tend to eliminate the s → t temporal flow. We then consider mixed temporal networks, which have some edges with specified availabilities and some edges with random availabilities; we show that it is #P-hard to compute the tails and expectations of the maximum temporal flow (which is now a random variable) in a mixed temporal network.

Original language | English (US) |
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Title of host publication | Algorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings |

Editors | Dimitris Fotakis, Aris Pagourtzis, Vangelis Th. Paschos |

Publisher | Springer Verlag |

Pages | 43-54 |

Number of pages | 12 |

ISBN (Print) | 9783319575858 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

Event | 10th International Conference on Algorithms and Complexity, CIAC 2017 - Athens, Greece Duration: May 24 2017 → May 26 2017 |

### 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 | 10236 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 10th International Conference on Algorithms and Complexity, CIAC 2017 |
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Country | Greece |

City | Athens |

Period | 5/24/17 → 5/26/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings*(pp. 43-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10236 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-57586-5_5