Stephane Rovedakis

Self-stabilizing minimum degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most @D^*+1, where @D^* is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge, our algorithm is the first self-stabilizing solution for the construction of a minimum degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e., the send/receive atomicity). The time complexity of our solution is O(mn^2logn) where m is the number of edges and n is the number of nodes. The memory complexity is O(@dlogn) in the send-receive atomicity model (@d is the maximal degree of the network).

A new self-stabilizing minimum spanning tree construction with loop-free property

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loopfree property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.

The first fully polynomial stabilizing algorithm for BFS tree construction

The construction of a spanning tree is a fundamental task in distributed systems which allows to resolve other tasks (i.e., routing, mutual exclusion, network reset). In this paper, we are interested in the problem of constructing a Breadth First Search (BFS) tree. Stabilization is a versatile technique which ensures that the system recover a correct behavior from an arbitrary global state resulting from transient faults. A fully polynomial algorithm has a round complexity in O(da) and a step complexity in O(nb) where d and n are the diameter and the number of nodes of the network and a and b are constants. We present the first fully polynomial stabilizing algorithm constructing a BFS tree under a distributed daemon. Moreover, as far as we know, it is also the first fully polynomial stabilizing algorithm for spanning tree construction. Its round complexity is in O(d2) and its step complexity is in O(n6). To our knowledge, since in general the diameter of a network is much smaller than the number of nodes (log(n) in average instead of n), this algorithm reaches the best compromise of the literature between the complexities in terms of rounds and in terms of steps.

Loop-free super-stabilizing spanning tree construction

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.

Fast Self-stabilizing Minimum Spanning Tree Construction

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is O(log2 n) bits and it converges in O(n2) rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor Θ(n), to the price of increasing the best known space complexity by a factor O(log n). The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only O(log2 n) bits.

Self-stabilizing minimum-degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most Δ*+ 1, where Δ* is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge our algorithm is the first self-stabilizing solution for the construction of a minimum-degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e. the send/receive atomicity). The time complexity of our solution is O(mn2 log n) where m is the number of edges and n is the number of nodes. The memory complexity is O(δ log n) in the send-receive atomicity model (δ is the maximal degree of the network).

A super-stabilizing log(n)-approximation algorithm for dynamic Steiner trees

This paper proposes a fully dynamic self-stabilizing algorithm for the dynamic Steiner tree problem. The Steiner tree problem aims at constructing a Minimum Spanning Tree (MST) over a subset of nodes called Steiner members, or Steiner group usually denoted S. Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks in the design of middleware architectures for the new emergent networks (e.g., P2P, sensor or adhoc networks). Our algorithm returns a log(|S|)-approximation of the optimal Steiner tree. It improves over existing solutions in several ways. First, it is fully dynamic, in other words it withstands the dynamism when both the group members and ordinary nodes can join or leave the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is super-stabilizing. 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.

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

This paper proposes a fully dynamic self-stabilizing algorithm for the Steiner tree problem. The Steiner tree problem aims at constructing a Minimum Spanning Tree (MST) over a subset of nodes called Steiner members, or Steiner group usually denoted S . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks in the design of middleware architectures for the new emergent networks (e.g. P2P, sensor or adhoc networks). Our algorithm returns a log|S |-approximation of the optimal Steiner tree. It improves over existing solutions in several ways. First, it is fully dynamic, in other words it withstands the dynamism when both the group members and ordinary nodes can join or leave the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is 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.

Evaluation of energy aware routing metrics for RPL

In the past few years, the Internet of Things is driving the need for extending the Internet to constrained devices, including sensors and actuators. The IPv6 Routing Protocol for Low power and lossy networks (RPL) is appearing as an emerging IETF standard especially tailored for Low Power Area Networks (6LoWPAN). RPL constructs a Directed Acyclic Graph (DAG) according to an objective function that governs the routing according to some metric(s) and constraint(s). In the last decade, several metrics and constraints have been proposed. In this paper, we survey RPL energy-aware routing metrics and we present to the best of our knowledge the first comparative evaluation considering grid and random topologies. Moreover, we consider in this evaluation two models for the exchange of messages: a model with no packet loss and a second one with 40% of packet loss. Our experiments show that multi-criteria metrics outperform other metrics.

A New Self-Stabilizing Minimum Spanning Tree Construction with Loop-Free Property

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Secondly, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date