In this paper we present time-optimal self-stabilizing algorithms for asynchronous distributed spanning tree computation in networks.

As communication networks grow, existing fault handling tools that involve global measures such as global time-outs or reset procedures become increasingly unaffordable, since their cost grows with the size of the network. Rather, for a fault handling mechanism to scale to large networks, its cost must depend only on the number of failed nodes Žwhich, thanks to today’s technology, grows much more slowly than the networks.. Moreover, it should allow the nonfaulty regions of the networks to continue their operation even during the recovery of the faulty parts. This paper introduces the concepts fault locality and fault-locally mendable problems, which are problems for which there are correction algorithms Žapplied after faults. whose cost depends only on the Ž unknown. number of faults. We show that any input-output problem is fault-locally mendable. The solution involves a novel technique combining data structures and ‘‘local votes’ ’ among nodes, which may be of interest in itself. � 1999 Academic Press * Alexander Goldberg lecturer.

) Alain Bui, 1 Ajoy K. Datta, 2 Franck Petit, 1 Vincent Villain 1 1 LaRIA, Universit e de Picardie Jules Verne, France 2 Department of Computer Science, University of Nevada, Las Vegas Abstract In this paper, we introduce the notion of snapstabilization. A snap-stabilizing algorithm protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification. So, a snap-stabilizing protocol is a self-stabilizing protocol which stabilizes in 0 steps. We propose a snap-stabilizing Propagation of Information with Feedback (PIF) scheme on a rooted tree network. We call this scheme Propagation of information with Feedback and Cleaning (PFC). We present two algorithms. The first one is a basic PFC scheme which is inherently snapstabilizing. However, it can be delayed O(h 2 ) steps (where h is the height of the tree) due to some undesirable local states. The second algorithm improves the worst delay of the basic PFC algori...

Baruch Awerbuch 12 , Boaz Patt-Shamir 2 , George Varghese 3 and Shlomi Dolev 45 1 Dept. of Computer Science, Johns Hopkins University 2 Lab. for Computer Science, MIT 3 Dept. of Computer Science, Washington University 4 Dept. of Computer Science, Texas A&M University 5 School of Computer Science, Carleton University Abstract. We describe a method for transforming asynchronous network protocols into protocols that can sustain any transient fault, i.e., become 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 protocol, any locally-checkable protocol can be made self-stabilizing. Our proof is constructive in the sense that we provide explicit code. The method applies to many practical network problems, including spanning tree construction, topology update, and virtual circuit setup. 1 Introduction A network protocol is called self-stabilizing (or stabilizing for sho...

We study the scenario where a transient fault hit f of the n nodes of a distributed system by corrupting their state. We consider the basic persistent bit problem, where the system is required to maintain a 0/1 value in the face of transient failures by means of replication. We give an algorithm to recover the value quickly: the value of the bit is recovered at all nodes in O(f) time units for an unknown f ! n=2. Moreover, complete state quiescence occurs in O(diam) time units, where diam denotes the actual diameter of the network. This means that the value persists indefinitely so long as any f ! n=2 faults are followed by \Omega\Gamma diam) fault-free time units. We prove matching lower bounds on both the output stabilization time and the state quiescence time. Using our persistent bit algorithm, we present a general transformer which takes a distributed non-reactive non-stabilizing protocol P , and produces a self-stabilizing protocol P 0 which solves the problem P solv...

A useful way to design simple and robust protocols is to make them self-stabilizing. A protocol

A local stabilizer protocol that takes any on-line or off-line distributed algorithm and converts it into a synchronous self-stabilizing algorithm with local monitoring and repairing properties is presented. Whenever the self-stabilizing version enters an inconsistent state, the inconsistency is detected, in O(1) time, and the system state is repaired in a local manner. The expected computation time that is lost during the repair process is proportional to the largest diameter of a faulty region. An extended abstract of this paper appeared in the Proc. of the 5th Israeli Symposium on Theory of Computing and Systems, June 1997 and a brief announcement in Proc. of the 16th Annual ACM Symp. on Principles of Distributed Computing, August 1997. y Computer Science Department, Tel-Aviv University, Tel-Aviv, 69978, Israel. Email: afek@math.tau.ac.il. z Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Partially supported by the Israeli m...

This paper presents a fast distributed algorithm to compute a small k-dominating set D (for any xed k) and its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log n).

. A self-stabilizing system is a distributed system which can tolerate any number and any type of faults in the history. After the last fault occurs the system starts to converge to a legitimate behavior. The self-stabilization property is very useful for systems in which processors may malfunction for a while and then recover. When there is a long enough period during which no processor malfunctions the system stabilizes. Dynamic systems are systems in which communication links and processors may fail and recover during normal operation. Such failures could cause partitioning of the system communication graph. The application of self-stabilizing protocols to dynamic systems is natural. Following the last topology change each connected component of the system stabilizes independently. We present time optimal self-stabilizing dynamic protocols for a variety of tasks including: routing, leader election and topology update. The protocol for each of those tasks stabilizes in \Theta(d) ti...

ght pulse synchronization that is uncorrelated to the actual clock values. The synchronized pulses are used as the events for re-synchronizing the clock values. 1 Introduction Overcoming failures that are not predictable in advance is most suitably addressed by tolerating Byzantine faults. It is the preferred fault model in order to seal o unexpected behavior within limitations on the number of concurrent faults. Most distributed tasks require the number of Byzantine faults, f , to abide by the ratio of 3f < n, where n is the network size. See [14] for impossibility results on several consensus related problems such as clock synchronization. Additionally, it makes sense to require such systems to resume operation after serious unpredictable events without the need for an outside intervention and/or a restart of the system from scratch. E.g. systems may occasionally experience This research was supported in part by Intel COMM Grant - Internet Network /Transport Layer & QoS Enviro