6 research outputs found
Universal Loop-Free Super-Stabilization
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
Self-Stabilization, Byzantine Containment, and Maximizable Metrics: Necessary Conditions
Self-stabilization is a versatile approach to fault-tolerance since it
permits a distributed system to recover from any transient fault that
arbitrarily corrupts the contents of all memories in the system. Byzantine
tolerance is an attractive feature of distributed systems that permits to cope
with arbitrary malicious behaviors. We consider the well known problem of
constructing a maximum metric tree in this context. Combining these two
properties leads to some impossibility results. In this paper, we provide two
necessary conditions to construct maximum metric tree in presence of transients
and (permanent) Byzantine faults
Memory requirements for silent stabilization
A self-stabilizing algorithm is silent if it converges to a glc)bal state after which the values stored in the com-munication registers are fixed. The silence property of self-stabilizing algorithms is a desirable property in terms of simplicity and communication overhead. In this work we show that no constant memory silent self-stabilizing algorithms exist for identification of the centers of a graph, leader election, and spanning tree construction. Lower bounds of Cl(log n) bits per communication register are obtained for each of the above tasks. The existence of a silent legitimate global state that uses less than log n bits per register is assumed. This legitimate global state is used to construct a silent global state that is illegitimate.
Stabilization of Maximal Metric Trees
We present a formal definition of routing metrics and provide the necessary and sufficient conditions for a routing metric to be optimizable along a tree. Based upon these conditions we present a generalization of the shortest path tree which we call the "maximal metric tree". We present a stabilizing protocol for constructing maximal metric trees. Our protocol demonstrates that the distance-vector routing paradigm may be extended to any metric that is optimizable along a tree and in a self-stabilizing manner. Examples of maximal metric trees include shortest path trees (distancevector) , depth first search trees, maximum flow trees, and reliability trees. 1. Introduction A number of papers have addressed stabilizing spanning tree construction and self-stabilizing shortest path tree protocols may be found in [DIM93, AKY90, AKM93, AG94]. Although not always explicit about this, most of the stabilizing tree protocols in the literature are based upon a distancevector approach. In the di..