Universal Loop-Free Super-Stabilization

TL;DR

This paper introduces a universal scheme for designing loop-free, super-stabilizing spanning tree protocols that optimize any tree metric, combining existing methods to preserve key properties without additional stabilization delay.

Contribution

It presents a novel composition approach that unifies super-stabilization, loop-freedom, and metric optimization in spanning tree protocols, applicable to various metrics.

Findings

Successfully applied to maximum-flow and minimum degree spanning trees

Preserves super-stabilization and loop-freedom without stabilization delay

Achieves metric optimization in a universal, compositional framework

Abstract

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree.