275 research outputs found

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

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    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)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+1OPT+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+1OPT+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)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

    Self-stabilizing cache placements in Manets

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    In ad-hoc networks mobile nodes communicate with each other using other nodes in the network as routers. Each node acts as a router, forwarding data packets for other nodes. There are many dynamic routing protocols to find routes between the communicating nodes. The bandwidth and power are limited in MANETs. Although routing is important in MANETs, the final task of MANETs is Data accessing. So, there is need to implement new techniques apart from routing for data access to save bandwidth and power. If some of the nodes in MANET is provided some of the services from internet Service Provider, then the other nodes also want to access these services. Then, there is a need for caching these services to reduce bandwidth and power; Caching the internet based services in MANETs is an important technique to reduce bandwidth, energy consumption and latency. If some of the nodes store the object data and code and acts as a cache proxies, then nodes near the cache proxies can get the requested data from the cache proxy rather than from a far away server node saving bandwidth and access latency; In this thesis research, we design a distributed self-stabilizing algorithm to place the caches in MANETs. If a node requests the service, it will search for the service and if that service is located in a node that is at a distance greater than D, then the requested node caches the data. In our algorithm, nodes that cache the same data will be at a distance greater than D. We also describe an algorithm to have the shortest path from the source of the data object to all the nodes that cache the same data in the network. This path is used to update the DATA that is cached in the nodes. We propose the algorithm for a single service or DATA. We can implement this algorithm in parallel for all the services available in the MANET; A self-stabilizing system has the ability to automatically recover to normal behavior in case of transient faults without a centralized control. The proposed algorithm does not require any initialization, that is, starting from an arbitrary state, it is guaranteed to satisfy its specification in finite steps. The protocol can handle various types of faults

    Making local algorithms efficiently self-stabilizing in arbitrary asynchronous environments

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    This paper deals with the trade-off between time, workload, and versatility in self-stabilization, a general and lightweight fault-tolerant concept in distributed computing.In this context, we propose a transformer that provides an asynchronous silent self-stabilizing version Trans(AlgI) of any terminating synchronous algorithm AlgI. The transformed algorithm Trans(AlgI) works under the distributed unfair daemon and is efficient both in moves and rounds.Our transformer allows to easily obtain fully-polynomial silent self-stabilizing solutions that are also asymptotically optimal in rounds.We illustrate the efficiency and versatility of our transformer with several efficient (i.e., fully-polynomial) silent self-stabilizing instances solving major distributed computing problems, namely vertex coloring, Breadth-First Search (BFS) spanning tree construction, k-clustering, and leader election

    Self-Stabilization in the Distributed Systems of Finite State Machines

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    The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

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

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    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 22 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

    Self-stabilizing interval routing algorithm with low stretch factor

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    A compact routing scheme is a routing strategy which suggests routing tables that are space efficient compared to traditional all-pairs shortest path routing algorithms. An Interval Routing algorithm is a compact routing algorithm which uses a routing table at every node in which a set of destination addresses that use the same output port are grouped into intervals of consecutive addresses. Self-stabilization is a property by which a system is guaranteed to reach a legitimate state in a finite number of steps starting from any arbitrary state. A self-stabilizing Pivot Interval Routing (PIR) algorithm is proposed in this work. The PIR strategy allows routing along paths whose stretch factor is at most five, and whose average stretch factor is at most three with routing tables of size O(n3/2log 23/2n) bits in total, where n is the number of nodes in the network. Stretch factor is the maximum ratio taken over all source-destination pairs between the length of the paths computed by the routing algorithm and the distance between the source and the destination. PIR is also an Interval Routing Scheme (IRS) using at most 2n( 1+lnn)1/2 intervals per link for the weighted graphs and 3n(1+ lnn)1/2 intervals per link for the unweighted graphs. The preprocessing stage of the PIR algorithm consists of nodelabeling and arc-labeling functions. The nodelabeling function re-labels the nodes with unique integers so as to facilitate fewer number of intervals per arc. The arc-labeling is done in such a fashion that the message delivery protocol takes an optimal path if both the source and the destination are located within a particular range from each other and takes a near-optimal path if they are farther from each other

    Self-stabilizing routing protocols

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    In systems made up of processors and links connecting the processors, the global state of the system is defined by the local variables of the individual processors. The set of global states can be defined as being either legal or illegal. A self-stabilizing system is one that forces a system from an illegal state to a global legal state without external interference, using a finite number of steps. This thesis will concentrate on application of self-stabilization to routing problems, in particular path identification, connectivity and methods involved in destinational routing. Traditional methods for creation of rooted paths to multiple destinations in a computer network involve the creation of spanning trees, and broadcasting information on the tree to be picked up by the individual nodes on the tree. The information for the creation of the tree are all sourced at the root, and the individual nodes update information from the centralized source. The self-stabilization model for networks allows the decision for a creation of a tree and message checking to occur automatically, locally, and more important, in contrast to traditional networks, asynchronously. The creation, message passing occur with a node and its immediate neighbor, and the tree, path is created based on this communicated data. In addition, the self-stabilization model eliminates the requisite initialization of traditional networks, i.e. given any arbitrary initial state the system (a given network) is guaranteed to stabilize to a legal global state, in the case of a broadcast network, a minimal spanning tree rooted at a source

    Disconnected components detection and rooted shortest-path tree maintenance in networks

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    International audienceMany articles deal with the problem of maintaining a rooted shortest-path tree. However, after some edge deletions, some nodes can be disconnected from the connected component VrV_r of some distinguished node rr. In this case, an additional objective is to ensure the detection of the disconnection by the nodes that no longer belong to VrV_r. We present a detailed analysis of a silent self-stabilizing algorithm. We prove that it solves this more demanding task in anonymous weighted networks with the following additional strong properties: it runs without any knowledge on the network and under the \emph{unfair} daemon, that is without any assumption on the asynchronous model. Moreover, it terminates in less than 2n+D2n+D rounds for a network of nn nodes and hop-diameter DD
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