Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems

In many wireless networks, there is no fixed physical backbone nor centralized network management. The nodes of such a network have to self-organize in order to maintain a virtual backbone used to route messages. Moreover, any node of the network can be a priori at the origin of a malicious attack. Thus, in one hand the backbone must be fault-tolerant and in other hand it can be useful to monitor all network communications to identify an attack as soon as possible. We are interested in the minimum \emph{Connected Vertex Cover} problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant approximation ratio of $2$ for this problem. In this paper, we propose a distributed and self-stabilizing version of their algorithm with the same approximation guarantee. To the best knowledge of the authors, it is the first distributed and fault-tolerant algorithm for this problem. The approach followed to solve the considered problem is based on the construction of a connected minimal clique partition. Therefore, we also design the first distributed self-stabilizing algorithm for this problem, which is of independent interest

Optimal Dynamic Distributed MIS

Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in their degrees. The result trivially applies for the dynamic distributed model, in which edges or nodes may be inserted or deleted. In this paper, we take a different approach which exploits locality to the extreme, and show how to update an MIS in a dynamic distributed setting, either \emph{synchronous} or \emph{asynchronous}, with only \emph{a single adjustment} and in a single round, in expectation. These strong guarantees hold for the \emph{complete fully dynamic} setting: Insertions and deletions, of edges as well as nodes, gracefully and abruptly. This strongly separates the static and dynamic distributed models, as super-constant lower bounds exist for computing an MIS in the former. Our results are obtained by a novel analysis of the surprisingly simple solution of carefully simulating the greedy \emph{sequential} MIS algorithm with a random ordering of the nodes. As such, our algorithm has a direct application as a $3$-approximation algorithm for correlation clustering. This adds to the important toolbox of distributed graph decompositions, which are widely used as crucial building blocks in distributed computing. Finally, our algorithm enjoys a useful \emph{history-independence} property, meaning the output is independent of the history of topology changes that constructed that graph. This means the output cannot be chosen, or even biased, by the adversary in case its goal is to prevent us from optimizing some objective function.Comment: 19 pages including appendix and reference

The network of stabilizing contacts in proteins studied by coevolutionary data

The primary structure of proteins, that is their sequence, represents one of the most abundant set of experimental data concerning biomolecules. The study of correlations in families of co--evolving proteins by means of an inverse Ising--model approach allows to obtain information on their native conformation. Following up on a recent development along this line, we optimize the algorithm to calculate effective energies between the residues, validating the approach both back-calculating interaction energies in a model system, and predicting the free energies associated to mutations in real systems. Making use of these effective energies, we study the networks of interactions which stabilizes the native conformation of some well--studied proteins, showing that it display different properties than the associated contact network

Improving Connectionist Energy Minimization

Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an improvement to the standard local activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm, called activate, is uniform and does not assume that the network is tree-like. It can identify tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid local minima along these trees. For acyclic networks, the algorithm is guaranteed to converge to a global minimum from any initial state of the system (self-stabilization) and remains correct under various types of schedulers. On the negative side, we show that in the presence of cycles, no uniform algorithm exists that guarantees optimality even under a sequential asynchronous scheduler. An asynchronous scheduler can activate only one unit at a time while a synchronous scheduler can activate any number of units in a single time step. In addition, no uniform algorithm exists to optimize even acyclic networks when the scheduler is synchronous. Finally, we show how the algorithm can be improved using the cycle-cutset scheme. The general algorithm, called activate-with-cutset, improves over activate and has some performance guarantees that are related to the size of the network's cycle-cutset.Comment: See http://www.jair.org/ for any accompanying file

The Evolution of Wikipedia's Norm Network

Social norms have traditionally been difficult to quantify. In any particular society, their sheer number and complex interdependencies often limit a system-level analysis. One exception is that of the network of norms that sustain the online Wikipedia community. We study the fifteen-year evolution of this network using the interconnected set of pages that establish, describe, and interpret the community's norms. Despite Wikipedia's reputation for \textit{ad hoc} governance, we find that its normative evolution is highly conservative. The earliest users create norms that both dominate the network and persist over time. These core norms govern both content and interpersonal interactions using abstract principles such as neutrality, verifiability, and assume good faith. As the network grows, norm neighborhoods decouple topologically from each other, while increasing in semantic coherence. Taken together, these results suggest that the evolution of Wikipedia's norm network is akin to bureaucratic systems that predate the information age.Comment: 22 pages, 9 figures. Matches published version. Data available at http://bit.ly/wiki_nor

A Self-Stabilizing K-Clustering Algorithm Using an Arbitrary Metric (Revised Version of RR2008-31)

32 pagesMobile ad hoc networks as well as grid platforms are distributed, changing, and error prone environments. Communication costs within such infrastructure can be improved, or at least bounded, by using k-clustering. A k-clustering of a graph, is a partition of the nodes into disjoint sets, called clusters, in which every node is distance at most k from a designated node in its cluster, called the clusterhead. A self-stabilizing asynchronous distributed algorithm is given for constructing a k-clustering of a connected network of processes with unique IDs and weighted edges. The algorithm is comparison-based, takes O(nk) time, and uses O(log n + log k) space per process, where n is the size of the network. This is the first distributed solution to the k-clustering problem on weighted graphs