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155
Computing on an Anonymous Ring
 Journal of the ACM
, 1988
"... Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is s ..."
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Cited by 87 (2 self)
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Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is shown that any of these functions can be computed in O(r?) messages in the asynchronous model. This is also proved to be a lower bound for such elementary functions as AND, SUM, and Orientation. In the synchronous model any computable function can be computed in O(n log n) messages. A ring can be oriented and start synchronized within the same bounds. The main contribution of this paper is a new technique for proving lower bounds in the synchronous model. With this technique tight lower bounds of O(nlogn) (for particular n) are proved for XOR, SUM, Orientation, and Start Synchronization. The technique is based on a stringproducing mechanism from formal language theory, first introduced by Thue to study squarefree words. Two methods for generalizing the synchronous lower bounds to arbitrary ring sizes are presented.
Easy Impossibility Proofs for Distributed Consensus Problems
 Distributed Computing
, 1986
"... Easy proofs are given, of the impossibility of solving several consensus problems (Byzantine agreement, weak agreement, Byzantine firing squad, approximate agreement and clock synchronization) in certain communication graphs. It is shown that, in the presence of m faults, no solution to these proble ..."
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Cited by 76 (8 self)
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Easy proofs are given, of the impossibility of solving several consensus problems (Byzantine agreement, weak agreement, Byzantine firing squad, approximate agreement and clock synchronization) in certain communication graphs. It is shown that, in the presence of m faults, no solution to these problems exists for communication graphs with fewer than 3m+ 1 nodes or less than 2m+l connectivity. While some of these results had previously been proved, the new proofs are much simpler, provide considerably more insight, apply to more general models of computation, and (particularly in the case of clock synchronization) significantly strengthen the results.
Symmetry Breaking In Distributed Networks
 Information and Computation
, 1981
"... Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To over ..."
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Cited by 70 (0 self)
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Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To overcome this difficulty, probabilistic algorithms are proposed. The algorithms may run forever but they terminate within finite time on the average. For the synchronous case several algorithms are presented: The simplest requires, on the average, the transmission of no more than 2.442n bits and O (n) time. More sophisticated algorithms trade time for communication complexity. If the processors work asynchronously then on the average O (nlogn) bits are transmitted. In the above cases the size of the ring was assumed to be known to all the processors. If the size is not known then finding it may be done only with high probability: any algorithm may yield incorrect results (with nonzero probabilit...
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.
Time Optimal SelfStabilizing Spanning Tree Algorithms
 In FSTTCS93 Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science, SpringerVerlag LNCS:761
, 1993
"... In this paper we present timeoptimal selfstabilizing algorithms for asynchronous distributed spanning tree computation in networks. ..."
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Cited by 61 (8 self)
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In this paper we present timeoptimal selfstabilizing algorithms for asynchronous distributed spanning tree computation in networks.
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.
Probabilistic SelfStabilization
, 1990
"... A probabilistic selfstabilizing algorithm for a ring of identical processes is presented; the number of processes in the ring is odd, the processes operate synchronously, and communication is unidirectional in the ring. The normal function of the algorithm is to circulate a single token in the ring ..."
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Cited by 51 (0 self)
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A probabilistic selfstabilizing algorithm for a ring of identical processes is presented; the number of processes in the ring is odd, the processes operate synchronously, and communication is unidirectional in the ring. The normal function of the algorithm is to circulate a single token in the ring. If the initial state of the ring is abnormal, i.e. the number of tokens differs from one, then execution of the algorithm results probabilistically in convergence to a normal state with one token. Keywords: Distributed Computing, Probabilistic Algorithms, SelfStabilization, Uniform Rings 0 Introduction A selfstabilizing algorithm for a ring of identical processes is required; the algorithm is to circulate exactly one token in the ring: if, in an initial state of ring, there are numerous tokens, then the algorithm is required to reduce the number of tokens until there is exactly one token. The solution presented in this paper is simple, inviting an informal example. Imagine seven boys, ...
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.
SelfStabilizing Distributed Constraint Satisfaction
, 1991
"... Distributed architectures and solutions are described for classes of constraint satisfaction problems, called network consistency problems. An inherent assumption of these architectures is that the communication network mimics the structure of the constraint problem. The solutions are required to be ..."
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Cited by 37 (3 self)
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Distributed architectures and solutions are described for classes of constraint satisfaction problems, called network consistency problems. An inherent assumption of these architectures is that the communication network mimics the structure of the constraint problem. The solutions are required to be selfstabilizing and to treat arbitrary networks, which makes them suitable for dynamic or errorprone environments. We first show that even for relatively simple constraint networks, such as rings, there is no selfstabilizing solution that guarantees convergence from every initial state of the system using a completely uniform, asynchronous model (where all processors are identical). An almostuniform, asynchronous, network consistency protocol with one specially designated node is shown and proven correct. We also show that some restricted topologies such as trees can accommodate the uniform, asynchronous model when neighboring nodes cannot take simultaneous steps. 1 Introduction Consid...