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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

Distributed computation of temporal twins in periodic undirected time-varying graphs

Résumé

Twin nodes in a static network capture the idea of being substitutes for each other for maintaining paths of the same length anywhere in the network. In dynamic networks, we model twin nodes over a time-bounded interval, noted $(\Delta,d)$-twins, as follows. A periodic undirected time-varying graph $\mathcal G=(G_t)_{t\in\mathbb N}$ of period $p$ is an infinite sequence of static graphs where $G_t=G_{t+p}$ for every $t\in\mathbb N$. For $\Delta$ and $d$ two integers, two distinct nodes $u$ and $v$ in $\mathcal G$ are $(\Delta,d)$-twins if, starting at some instant, the outside neighbourhoods of $u$ and $v$ has non-empty intersection and differ by at most $d$ elements for $\Delta$ consecutive instants. In particular when $d=0$, $u$ and $v$ can act during the $\Delta$ instants as substitutes for each other in order to maintain journeys of the same length in time-varying graph $\mathcal G$. We propose a distributed deterministic algorithm enabling each node to enumerate its $(\Delta,d)$-twins in $2p$ rounds, using messages of size $O(\delta_\mathcal G\log n)$, where $n$ is the total number of nodes and $\delta_\mathcal G$ is the maximum degree of the graphs $G_t$'s. Moreover, using randomized techniques borrowed from distributed hash function sampling, we reduce the message size down to $O(\log n)$ w.h.p.
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Dates et versions

hal-04559327 , version 1 (25-04-2024)

Identifiants

  • HAL Id : hal-04559327 , version 1

Citer

Lina Azerouk, Binh-Minh Bui-Xuan, Camille Palisoc, Maria Potop-Butucaru, Massinissa Tighilt. Distributed computation of temporal twins in periodic undirected time-varying graphs. 2024. ⟨hal-04559327⟩
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