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

Locally finite groups containing a 2 -element with Chernikov centralizer

Suppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ⟨g⟩ has nilpotent centralizer, then G has a soluble subgroup of finite index

Efficient Scheduling of Data-Harvesting Trees

Many applications in sensor networks demand for energy and time optimal routing of data towards a sink. In this work we present mechanisms to set up energy and time efficient TDMA schedules for a given routing tree under very strict limitations: Nodes have only a constant size memory and must agree on a schedule using only a minimum of communication for set up: Each node is only allowed to send a single message to each of its neighbors. We propose and analyze solutions in two different interference models. We show that, despite these tight restrictions, it is possible to compute energy optimal schedules which are almost time optimal and time optimal schedules which are almost energy optimal in the total interference model and we describe a 4-approximative algorithm in the k-local interference model. We also show how to extend these mechanisms to settings with packet loss, while still guaranteeing bounds on energy consumption

The Heathland Experiment: Results And Experiences

This paper reports on the experience gained during a realworld deployment of a sensor network based on the ESB platform in the heathlands of Northern Germany. The goal of the experiment was to gain a deeper insight into the problems of real deployments as opposed to simulated networks. The focus of this report is on the quality of radio links and the influence of the link quality on multi-hop routing

A Self-stabilizing Algorithm for Edge Monitoring Problem

International audienceSelf-monitoring is a simple and effective mechanism for the security of wireless sensor networks (WSNs), especially to cope against compromised nodes. A node v can monitor an edge e if both end-nodes of e are neighbors of v; i.e., e together with v forms a triangle in thegraph. Moreover, some edges need more than one monitor. Finding a set of monitoring nodes satisfying all monitoring constraints is called the edge-monitoring problem. The minimum edge-monitoring problem is long known to be NP-complete. In this paper, we present a novelsilent self-stabilizing algorithm for computing a minimal edge-monitoring set. Correctness and termination are proven for the unfair distributed scheduler