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

TL;DR

This paper presents a fully dynamic, self-stabilizing, and superstabilizing distributed algorithm that maintains a logarithmic-approximate Steiner tree efficiently in changing networks, supporting robust communication primitives.

Contribution

It introduces a novel superstabilizing algorithm with a th approximation ratio for dynamic Steiner trees, improving robustness and stability over prior solutions.

Findings

Achieves th approximation ratio for dynamic Steiner trees.

Supports dynamic changes in network and group membership.

Maintains service during stabilization after network modifications.

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.