### Abstract

We introduce temporal flows on temporal networks. We show that one can find the maximum amount of flow that can pass from a source vertex s to a sink vertex t up to a given time in Polynomial time. We provide a static Time-Extended network (TEG) of polynomial size to the input, and show that temporal flows can be decomposed into flows, each moving through a single s-t temporal path. We then examine the case of unbounded node buffers. We prove that the maximum temporal flow is equal to the value of the minimum temporal s-t cut. We partially characterise networks with random edge availabilities that tend to eliminate the s-t temporal flow. We also consider mixed temporal networks, where some edges have specified availabilities and some edges have random availabilities; we define the truncated expectation of the maximum temporal flow and show that it is #P-hard to compute it.

Original language | English (US) |
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Pages (from-to) | 46-60 |

Number of pages | 15 |

Journal | Journal of Computer and System Sciences |

Volume | 103 |

DOIs | |

State | Published - Aug 2019 |

Externally published | Yes |

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### Keywords

- Edge availability
- Network flows
- Random input
- Temporal networks

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Journal of Computer and System Sciences*,

*103*, 46-60. https://doi.org/10.1016/j.jcss.2019.02.003