## Connectivity and Inference Problems for Temporal Networks (2000)

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Venue: | J. Comput. Syst. Sci |

Citations: | 49 - 3 self |

### BibTeX

@INPROCEEDINGS{Kempe00connectivityand,

author = {David Kempe and Jon Kleinberg and Amit Kumar},

title = {Connectivity and Inference Problems for Temporal Networks},

booktitle = {J. Comput. Syst. Sci},

year = {2000},

pages = {2002}

}

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### Abstract

Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated. ” We will call such a graph a temporal network. To model the notion that information in such a network “flows ” only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the

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Citation Context ...rmation has learned, since it came along several “independent” trajectories through the network [16, 18]. In standard graphs, the existence of node-disjoint paths is characterized by Menger’s Theorem =-=[15]-=-: the maximum number of node-disjoint -� paths is equal to the minimum number of nodes needed to separate � from � . But there � is no analogue of this theorem for arbitrary temporal networks. As obse... |

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Citation Context ...etail below. Background.. There is a large literature on gossiping and broadcasting algorithms in networks; see [11] for a survey. Two paradigmatic problems in this area are (i) the Telephone Problem =-=[2, 5, 8, 10, 20]-=-, in which we seek a way for � individuals to each transmit a distinct piece of information to everyone else using the minimum number of person-to-person phone calls; and (ii) the Minimum Broadcast Ti... |

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Citation Context ...igated by studying the time-respecting paths in a network. Scheduled Transportation Networks. Finally, many of the same issues arise in the context of scheduled transportation, such as airline travel =-=[4]-=-. We may be given a network of airports, with edges labeled by the time(s) at which flights depart and arrive; the timerespecting paths are those that can be feasibly used by a traveler in this networ... |

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Citation Context ...etail below. Background.. There is a large literature on gossiping and broadcasting algorithms in networks; see [11] for a survey. Two paradigmatic problems in this area are (i) the Telephone Problem =-=[2, 5, 8, 10, 20]-=-, in which we seek a way for � individuals to each transmit a distinct piece of information to everyone else using the minimum number of person-to-person phone calls; and (ii) the Minimum Broadcast Ti... |

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Citation Context ...specting paths � from � to ? If this is the case, we can be more confident in the accuracy of the � information has learned, since it came along several “independent” trajectories through the network =-=[16, 18]-=-. In standard graphs, the existence of node-disjoint paths is characterized by Menger’s Theorem [15]: the maximum number of node-disjoint -� paths is equal to the minimum number of nodes needed to sep... |

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