A Superstabilizing $\log(n)$-Approximation Algorithm for Dynamic Steiner Trees

Lélia Blin 1, 2, * Maria Gradinariu Potop-Butucaru 3, * Stephane Rovedakis 2, *
* Corresponding author
1 NPA - Networks and Performance Analysis
LIP6 - Laboratoire d'Informatique de Paris 6
3 Regal - Large-Scale Distributed Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group) . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks for the new emergent networks (e.g. P2P, sensor or adhoc networks). The cost of the solution returned by our algorithm is at most $\log |S|$ times the cost of an optimal solution, where $S$ is the group of members. Our algorithm improves over existing solutions in several ways. First, it tolerates the dynamism of both the group members and the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is \emph{superstabilizing}. That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it keeps offering the Steiner tree service during the stabilization time to all members that have not been affected by this modification.
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Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis. A Superstabilizing $\log(n)$-Approximation Algorithm for Dynamic Steiner Trees. 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2009), Nov 2009, Lyon, France. pp.133-148, ⟨10.1007/978-3-642-05118-0_10⟩. ⟨hal-00363003⟩

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