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68
Uniform dynamic selfstabilizing leader election
 IEEE Transactions on Parallel and Distributed Systems
, 1997
"... Abstract—A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The selfstabilization property makes the system tolerant to faults in which processors exhibit a ..."
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Cited by 100 (10 self)
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Abstract—A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The selfstabilization property makes the system tolerant to faults in which processors exhibit a faulty behavior for a while and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next faulty period is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic selfstabilizing protocols for leader election under readwrite atomicity. Our protocols use randomization to break symmetry. The leader election protocol stabilizes in OaD'log nf time when the number of the processors is unknown and OaD'f, otherwise. Here D denotes the maximal degree of a node, ' denotes the diameter of the graph and n denotes the number of processors in the graph. We introduce selfstabilizing protocols for synchronization that are used as building blocks by the leaderelection algorithm. We conclude this work by presenting a simple, uniform, selfstabilizing ranking protocol. Index Terms—Selfstabilizing systems, leader election, distributed algorithms, randomized distributed algorithms, synchronization. 1
Computing on anonymous networks, part I: characterizing the solvable cases
 IEEE TRANSACTION ON PARALLEL AND DISTRIBUTED COMPUTING
, 1996
"... In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a g ..."
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Cited by 66 (3 self)
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In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a given network, the above problems may or may not be solvable, depending on the amount of information about the attributes of the network made available to the processors. Some possibilities are: (1) no network attribute information at all is available, (2) an upper bound on the number of processors in the network is available, (3) the exact number of processors in the network is available, and (4) the topology of the network is available. In terms of a new graph property called “symmetricity, ” in each of the four cases (1)–(4) above, we characterize the class of networks on which each of the four problems (a)–(d) is solvable. We then relate the symmetricity of a network to its 1 and 2factors.
Electing a Leader in a Synchronous Ring
, 1987
"... The problem of electing a leader in a synchronous ring of n processon is considered. Both positive and negative results are obtained. On the one hand, if processor IDs are chosen from some countable set, then there is an algorithm that uses only O(n) messages in the wont case. On the other hand, any ..."
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Cited by 52 (3 self)
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The problem of electing a leader in a synchronous ring of n processon is considered. Both positive and negative results are obtained. On the one hand, if processor IDs are chosen from some countable set, then there is an algorithm that uses only O(n) messages in the wont case. On the other hand, any algorithm that is restricted to use only comparisons of IDs requires fl(n log n) messages in the worst case. Alternatively, if the number of rounds is required to be bounded by some t in the wont case, and lDs are chosen from any set having at least f(n, t) elements, for a certain very fastgrowing functionf then any algorithm requires fl(n log n) messages in the wont case.
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 44 (4 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
Sense of Direction: Definitions, Properties and Classes
"... An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named Sense of Direction. In spite of the large amount of investigati ..."
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Cited by 35 (10 self)
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An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named Sense of Direction. In spite of the large amount of investigations, and of the obvious practical importance, a formal characterization of this property did not exist. In this paper, we finally provide a formal definition of sense of direction, making explicit the very specific relationship between three factors: the labeling, the topological structure, and the local view that an entity has of the system. In a way, sense of direction is the capability of a node in the system to use the labeling to translate the local view of its neighbors into its own. Using the formal definition as an observational platform, we describe several properties which allow the translation process to be possible beyond the immediate neighborhood. Finally, we identify four gene...
SelfStabilizing Symmetry Breaking in ConstantSpace (Extended Abstract)
 IN PROC. 24TH ACM SYMP. ON THEORY OF COMPUTING
, 1992
"... We investigate the problem of selfstabilizing roundrobin token management scheme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic (coinflipping) finite state machine which sends and receives messages. We show that the solution to th ..."
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Cited by 30 (5 self)
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We investigate the problem of selfstabilizing roundrobin token management scheme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic (coinflipping) finite state machine which sends and receives messages. We show that the solution to this problem is equivalent to symmetry breaking (i.e., leader election). Requiring only constantsize messages and messagepassing model has practical implications: our solution can be implemented in highspeed networks using a universal fast hardware switches (i.e., finite state machines) of size independent of the size of the network. Our automatabased messagepassing model has inherent deadlock possibility (i.e., when all processors are waiting for a message) which we assume is detected by an external timeout mechanism. Provided that there is no deadlock to begin with, we show how starting from an arbitrary configuration, the system never enters a deadlock state and further stabilizes in p...
Sense of Direction in Distributed Computing
 In 12th International Symposium on Distributed Computing (DISC
, 1998
"... Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this pr ..."
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Cited by 29 (10 self)
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Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this property are still not known; in fact, the ongoing investigations continue to bring new (often surprising) results, to establish unsuspected links with other research and/or application areas, and to pose more questions than they answer. The aim of this paper is to provide a view of the current status of research, describing some of the relevant results, and providing pointers to future research directions. 1 Introduction In its more general formulation, a distributed system is a collection of computational entities communicating by exchanging finite amounts of information, which we shall call messages. The exact nature of the entities (i.e., processors, processes, network nodes, agents,...
Sense of Direction: Formal Definitions and Properties
, 1994
"... . In this paper, we provide a formal definition of Sense of Direction. In particular, we define the properties whose presence in a labeling make possible the reduction in communication complexity uncovered by the previous investigations. This is achieved by identifying the mechanisms which operate i ..."
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Cited by 28 (15 self)
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. In this paper, we provide a formal definition of Sense of Direction. In particular, we define the properties whose presence in a labeling make possible the reduction in communication complexity uncovered by the previous investigations. This is achieved by identifying the mechanisms which operate in the reduction, and determining the conditions for the existence of those mechanisms. Based on the formal definition, we have identified and defined four general classes of labelings and analyzed their properties. These classes include all the labelings used in the literature. 1 Introduction The ultimate goal of the research in Distributed Computing is to understand the nature, the properties and the limits of computing in a system of autonomous communicating agents. To this end, it is crucial to identify those factors which are significant for the computability and the communication complexity of problems. A distributed system is a collection of processing entities (e.g., processors) conn...
Gap Theorems for Distributed Computation
 SIAM Journal on Computing
, 1986
"... lower bounds, gap theorem. Consider a bidirectional ring of n identical processors that communicate asynchronously. The processors have no identifiers and hence the ring is called anonymous. Each processor receives an input letter, and the ring is to compute a function of the circular input string. ..."
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Cited by 25 (2 self)
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lower bounds, gap theorem. Consider a bidirectional ring of n identical processors that communicate asynchronously. The processors have no identifiers and hence the ring is called anonymous. Each processor receives an input letter, and the ring is to compute a function of the circular input string. If the function value is constant for all input strings, then the processors do not need to send any messages. On the other hand, we prove that any deterministic algorithm that computes any nonconstant function for anonymous rings requires Ω(n logn) bits of communication for some input string. We also exhibit nonconstant functions that require O (n logn) bits of communication for every input string. The same gap for the bit complexity of nonconstant functions remains even if the processors have distinct identifier, provided that the identifiers are taken from a large enough domain. When the communication is measured in messages rather than bits, the results change. We present a nonconstant function that can be computed with O (n log*n) messages on an anonymous ring. 1.