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Computing Temporal Twins in Time Logarithmic in History Length

Abstract : A temporal graph G is a sequence of static graphs indexed by a set of integers T representing time instants. For ∆ an integer, a pair of ∆-twins is a pair of vertices u \neg v which, starting at some time instant, have exactly the same neighbourhood outside {u, v} for ∆ consecutive instants. We address the enumeration problem of all pairs of ∆-twins in G, such that the overall runtime depends the least on the history length, namely max{t : G_t ∈ G not empty } − min{t : G_t ∈ G not empty }. We give logarithmic solutions, using red-black tree data structure. Numerical analysis of our implementation on graphs collected from real world data scales up to 10^8 history length.
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https://hal.archives-ouvertes.fr/hal-02997890
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Submitted on : Tuesday, November 10, 2020 - 11:56:52 AM
Last modification on : Sunday, June 26, 2022 - 2:56:29 AM
Long-term archiving on: : Friday, February 12, 2021 - 12:16:51 PM

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  • HAL Id : hal-02997890, version 1

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Binh-Minh Bui-Xuan, Hugo Hourcade, Cédric Miachon. Computing Temporal Twins in Time Logarithmic in History Length. Complex Networks 2020, Dec 2020, Madrid, Spain. ⟨hal-02997890⟩

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