19,236 research outputs found

    Universal Loop-Free Super-Stabilization

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    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

    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

    Randomization Adaptive Self-Stabilization

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    We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from an infinite number to a bounded number. The scheme is applicable to the cases in which there exits a local predicate for each node, such that global consistency is implied by the union of the local predicates. We demonstrate our scheme over the token circulation algorithm of Herman and the recent constant time Byzantine self-stabilizing clock synchronization algorithm by Ben-Or, Dolev and Hoch. The application of our scheme results in the first constant time Byzantine self-stabilizing clock synchronization algorithm that uses a bounded number of random bits

    Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

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    We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of O(nlogΔ)O(n\log \Delta) bits per node and O(nD)O(nD) respectively, where Δ\Delta is the highest degree of a node, nn is the number of nodes and DD is the diameter of the network. In contrast, our algorithm has a space complexity of O(logn)O(\log n) bits per node, which is optimal for silent-stabilizing spanning trees and runs in O(n)O(n) time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

    Fast and compact self-stabilizing verification, computation, and fault detection of an MST

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    This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes it for improving the time complexity significantly, while maintaining space optimality. As a result, we show that optimizing the memory size carries at most a small cost in terms of time, in the context of Minimum Spanning Tree (MST). That is, we present algorithms that are both time and space efficient for both constructing an MST and for verifying it.This involves several parts that may be considered contributions in themselves.First, we generalize the notion of local proofs, trading off the time complexity for memory efficiency. This adds a dimension to the study of distributed local proofs, which has been gaining attention recently. Specifically, we design a (self-stabilizing) proof labeling scheme which is memory optimal (i.e., O(logn)O(\log n) bits per node), and whose time complexity is O(log2n)O(\log ^2 n) in synchronous networks, or O(Δlog3n)O(\Delta \log ^3 n) time in asynchronous ones, where Δ\Delta is the maximum degree of nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991). We also show that Ω(logn)\Omega(\log n) time is necessary, even in synchronous networks. Another property is that if ff faults occurred, then, within the requireddetection time above, they are detected by some node in the O(flogn)O(f\log n) locality of each of the faults.Second, we show how to enhance a known transformer that makes input/output algorithms self-stabilizing. It now takes as input an efficient construction algorithm and an efficient self-stabilizing proof labeling scheme, and produces an efficient self-stabilizing algorithm. When used for MST, the transformer produces a memory optimal self-stabilizing algorithm, whose time complexity, namely, O(n)O(n), is significantly better even than that of previous algorithms. (The time complexity of previous MST algorithms that used Ω(log2n)\Omega(\log^2 n) memory bits per node was O(n2)O(n^2), and the time for optimal space algorithms was O(nE)O(n|E|).) Inherited from our proof labelling scheme, our self-stabilising MST construction algorithm also has the following two properties: (1) if faults occur after the construction ended, then they are detected by some nodes within O(log2n)O(\log ^2 n) time in synchronous networks, or within O(Δlog3n)O(\Delta \log ^3 n) time in asynchronous ones, and (2) if ff faults occurred, then, within the required detection time above, they are detected within the O(flogn)O(f\log n) locality of each of the faults. We also show how to improve the above two properties, at the expense of some increase in the memory

    Automated Synthesis of Distributed Self-Stabilizing Protocols

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    In this paper, we introduce an SMT-based method that automatically synthesizes a distributed self-stabilizing protocol from a given high-level specification and network topology. Unlike existing approaches, where synthesis algorithms require the explicit description of the set of legitimate states, our technique only needs the temporal behavior of the protocol. We extend our approach to synthesize ideal-stabilizing protocols, where every state is legitimate. We also extend our technique to synthesize monotonic-stabilizing protocols, where during recovery, each process can execute an most once one action. Our proposed methods are fully implemented and we report successful synthesis of well-known protocols such as Dijkstra's token ring, a self-stabilizing version of Raymond's mutual exclusion algorithm, ideal-stabilizing leader election and local mutual exclusion, as well as monotonic-stabilizing maximal independent set and distributed Grundy coloring
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