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

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

log(n)-approximation d'un arbre de Steiner auto-stabilisant et dynamique

National audienceCe travail est motivé entre autre, par le maintient distribué d'infrastructures optimisées pour la communication d'un groupe d'utilisateurs dispersé sur un réseau dynamique. Les domaines d'application typiques de telles structures sont les systèmes de publish/subscribe, bases de données distribuées, systèmes multicasts. Dans ce papier nous décrivons un algorithme distribué qui construit et maintient un arbre de Steiner approché connectant un groupe dynamique de membres dispersé sur un réseau dynamique. Le coût de la solution retournée par notre algorithme est au plus $\log |S|$ fois le coût de la solution optimale, $S$ étant le groupe de membres à interconnecter. Notre algorithme améliore les solutions existantes de plusieurs façons. Premièrement, il tolère le dynamisme des membres et du réseau, autrement dit les membres peuvent rejoindre ou quitter le groupe et les noeuds ou liens du réseau peuvent apparaître ou disparaître du réseau. Deuxièmement notre algorithme est auto-stabilisant, en d'autres termes il tolère les fautes transitoires. Enfin, notre algorithme est super-stabilisant, ce qui signifie que l'on garantie des propriétés sur la structure construite durant la convergence de l'algorithme et malgré le dynamisme du réseau

Automatic construction, maintenance, and optimization of dynamic agent organizations

The goal of this dissertation is to generate organizational structures that increase the overall performance of a multiagent coalition, subject to the system's complex coordination requirements and maintenance of a certain operating point. To this end, a generalized framework capable of producing distributed approximation algorithms based on the new concept of multidirectional graph search is proposed and applied to a family of connectivity problems. It is shown that a wide variety of seemingly unrelated multiagent organization problems live within this family. Su cient conditions are identi ed in which the approach is guaranteed to discover a solution that is within a constant factor of the cost of the optimal solution. The procedure is guaranteed to require no more than linear|and in some well de ned cases logarithmic|communication rounds. A number of examples are given as to how the framework can be applied to create, maintain, and optimize multiagent organizations in the context of real world problems. Finally, algorithmic extensions are introduced that allow for the framework to handle problems in which the agent topology and/or coordination constraints are dynamic, without signi cant consequences to the general runtime, memory, and quality guarantees.Ph.D., Computer Science -- Drexel University, 201

Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction

Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we present a space-optimal \emph{silent} self-stabilizing construction of minimum-degree spanning trees in this model. Computing a spanning tree with minimum degree is NP-hard. Therefore, we actually focus on constructing a spanning tree whose degree is within one from the optimal. Our algorithm uses registers on $O(\log n)$ bits, converges in a polynomial number of rounds, and performs polynomial-time computation at each node. Specifically, the algorithm constructs and stabilizes on a special class of spanning trees, with degree at most $OPT+1$. Indeed, we prove that, unless NP $=$ coNP, there are no proof-labeling schemes involving polynomial-time computation at each node for the whole family of spanning trees with degree at most $OPT+1$. Up to our knowledge, this is the first example of the design of a compact silent self-stabilizing algorithm constructing, and stabilizing on a subset of optimal solutions to a natural problem for which there are no time-efficient proof-labeling schemes. On our way to design our algorithm, we establish a set of independent results that may have interest on their own. In particular, we describe a new space-optimal silent self-stabilizing spanning tree construction, stabilizing on \emph{any} spanning tree, in $O(n)$ rounds, and using just \emph{one} additional bit compared to the size of the labels used to certify trees. We also design a silent loop-free self-stabilizing algorithm for transforming a tree into another tree. Last but not least, we provide a silent self-stabilizing algorithm for computing and certifying the labels of a NCA-labeling scheme