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Computing Small Temporal Modules in Time Logarithmic in History Length

Abstract : A temporal graph G is a sequence of static graphs indexed by a set of integers representing time instants. Given ∆ an integer, a ∆-module is a set of vertices A having the same neighbourhood outside of A for ∆ consecutive instants. We address specific cases of ∆-module enumeration, when |A| = 2 or when ∆ = ∞. Our main parameter for time complexity analysis is the history length τ = max{t : G t ∈ G not empty } − min{t : G t ∈ G not empty }. Using red-black tree data structure, we give solutions to above enumeration problems in time logarithmic in τ. For the general ∆-module enumeration problem, we give a pre-processing using overlapping properties of minimal ∆modules. Numerical analysis of our implementation on graphs collected from real world data scales up to a history length of 10 8 time instants 1. Keywords graph theory • historical data • modular decomposition • temporal graph Supported by Courtanet-Sorbonne Université convention C19.0665 and ANRT grant 2019.0485.
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https://hal.archives-ouvertes.fr/hal-03431380
Contributor : Binh-Minh Bui-Xuan Connect in order to contact the contributor
Submitted on : Tuesday, November 16, 2021 - 4:18:27 PM
Last modification on : Sunday, June 26, 2022 - 3:19:43 AM
Long-term archiving on: : Thursday, February 17, 2022 - 8:11:42 PM

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  • HAL Id : hal-03431380, version 1

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Binh-Minh Bui-Xuan, Hugo Hourcade, Cédric Miachon. Computing Small Temporal Modules in Time Logarithmic in History Length. Social Network Analysis and Mining, Springer, In press. ⟨hal-03431380⟩

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