Conference Paper

Self-Stabilization by Local Checking and Global Reset (Extended Abstract)

DOI: 10.1007/BFb0020443 Conference: Distributed Algorithms, 8th International Workshop, WDAG '94, Terschelling, The Netherlands, September 29 - October 1, 1994, Proceedings
Source: DBLP


We describe a method for transforming asynchronous network protocols into protocols that can sustain any transient fault, i.e., be come self-stabilizing. We combine the known notion of local checking with a new notion of internal reset, and prove that given any self-stabilizing internal reset protoco l, any locally-checkable protocol can be made self-stabilizing. Our proof is construct ive in the sense that we provide explicit code. The method applies to many practical network problems, including spanning tree construction, topology update, an d virtual circuit setup.

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    • "Note that reset is beyond the scope of the current paper (that deals with unbounded counters) and is mentioned here only as a motivation. However, such multiple protocols were suggested in the literature, for example, see [3], [9], [7], [45], [51], [23], [50], [13], [21], [5] to name just a few. Moreover, it was noted in [1] that it is rather easy to translate a self-stabilizing spanning tree construction protocol into a reset protocol. "
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    ABSTRACT: A synchronizer with a phase counter (sometimes called asynchronous phase clock) is an asynchronous distributed algorithm, where each node maintains a local "pulse counter" that simulates the global clock in a synchronous network. In this paper, we present a time-optimal self-stabilizing scheme for such a synchronizer, assuming unbounded counters. We give a simple rule by which each node can compute its pulse number as a function of its neighbors' pulse numbers. We also show that some of the popular correction functions for phase clock synchronization are not self-stabilizing in asynchronous networks. Using our rule, the counters stabilize in time bounded by the diameter of the network, without invoking global operations. We argue that the use of unbounded counters can be justified by the availability of memory for counters that are large enough to be practically unbounded and by the existence of reset protocols that can be used to restart the counters in some rare cases where faults will make this necessary.
    Preview · Article · Aug 2007 · IEEE Transactions on Dependable and Secure Computing
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    • "[16], Awerbuch et al. extend this idea to deal with problems that can be locally checked but require global correction to achieve self-stabilization. "
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    ABSTRACT: A commonly desired feature of large-scale, multihop, wireless sensor networks (WSNs) is the ability to reconfigure them after deployment. This reconfiguration could be as simple as changing a single parameter or as complex as replacing the entire application. Several protocols have been proposed to enable reconfiguration in WSNs, most of which use version numbers to distinguish new configurations from old ones. Due to constraints on memory and message sizes, version numbers are bounded and use wraparound arithmetic to handle rollover. While this simple scheme works well in the common case, we identify in this paper, a serious version management problem in existing protocols due to which a reconfiguration operation may never stabilize. We analyze potential causes of this problem and its effects on the quality and lifetime of the network. Through extensive simulations and experiments, we demonstrate the significant likelihood of this problem occurring in real deployments. Finally, we provide a solution to this problem using a novel approach which we call Human-In-The-Loop stabilization. Our stabilizing reconfiguration protocol uses local detectors and correctors that can detect version inconsistencies and prevent their propagation in a timely and efficient manner, while ultimately allowing the human operator to restore the network to the correct configuration. Our simulations and experiments also demonstrate the performance benefits of our solution over previous, nonstabilizing protocols.
    Full-text · Conference Paper · Jul 2006
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    • "There are also some other differences between the models. In [13] [12] [11] it is assumed that a vertex can read a state of a link port of a neighboring vertex. We assume that all the neighbors of a vertex v can see the same label of v. "
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    ABSTRACT: This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as “how expensive is local verification?” and more specifically, “how expensive is local verification compared to computation?” A suitable model is introduced in which these questions are studied in terms of the number of bits a vertex needs to communicate. The model includes the definition of a proof labeling scheme (a pair of algorithms- one to assign the labels, and one to use them to verify that the global property holds). In addition, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the bit complexity of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity, in the context of proof labeling schemes. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables the verification to be less costly sometimes, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify it, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind. KeywordsDistributed networks-Proof labels-Property verification-Self stabilization
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