## Symmetry Breaking In Distributed Networks (1981)

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Venue: | Information and Computation |

Citations: | 74 - 0 self |

### BibTeX

@ARTICLE{Itai81symmetrybreaking,

author = {Alon Itai and Michael Rodeh},

title = {Symmetry Breaking In Distributed Networks},

journal = {Information and Computation},

year = {1981},

volume = {88},

pages = {150--158}

}

### Years of Citing Articles

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### Abstract

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...

### Citations

208 |
Local and global properties in networks of processors
- Angluin
- 1980
(Show Context)
Citation Context ..., and discuss two global problems: (i) Choosing a leader --- a uniquely designated processor, such that each processor knows whether it is the leader; (ii) Finding n --- the size of the ring. Angluin =-=[A]-=- has investigated the problem of choosing a leader using Milne and Milner's [MM] model for distributed systems (her results may be applied to other models as well). She has shown that there exists no ... |

104 |
Probabilistic algorithms
- Rabin
- 1976
(Show Context)
Citation Context ...oneous result. Global information (such as knowing the size of the ring) does not always help. Since either termination or correctness must be compromised, we shall construct probabilistic algorithms =-=[R1]-=- --- algorithms which usually terminate with a correct result. Thus, we assume that even though the processors are identical, each has an independent random number generator. (For a use of probabilist... |

93 |
An improved algorithm for decentralized extrema-finding in circular configurations of processes
- Chang, Roberts
- 1979
(Show Context)
Citation Context ...f choosing a leader is easier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], =-=[CR]-=-, [DKR], [F1], [HS], [L], [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has comput... |

93 |
Distributed systems: Towards a formal approach
- Lann
- 1977
(Show Context)
Citation Context ...sier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], [CR], [DKR], [F1], [HS], =-=[L]-=-, [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has computed the required value it... |

56 | An O(n log n) unidirectional distributed algorithm for extrema finding in a circle
- Dolev, Klawe, et al.
- 1982
(Show Context)
Citation Context ...sing a leader is easier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], [CR], =-=[DKR]-=-, [F1], [HS], [L], [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has computed the ... |

51 |
Decentralized extrema-finding in circular configurations of processes
- Hirschberg, Sinclair
- 1980
(Show Context)
Citation Context ... is easier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], [CR], [DKR], [F1], =-=[HS]-=-, [L], [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has computed the required val... |

50 |
An O(n log n) unidirectional algorithm for the circular extrema problem
- Peterson
- 1982
(Show Context)
Citation Context ...in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], [CR], [DKR], [F1], [HS], [L], =-=[Pe]-=-). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has computed the required value it is aw... |

44 |
Concurrent Processes and Their Syntax
- Milne, Milner
- 1977
(Show Context)
Citation Context ...ted processor, such that each processor knows whether it is the leader; (ii) Finding n --- the size of the ring. Angluin [A] has investigated the problem of choosing a leader using Milne and Milner's =-=[MM]-=- model for distributed systems (her results may be applied to other models as well). She has shown that there exists no single program which runs on all the vertices of a ring of arbitrary size and de... |

40 |
A Compositional Approach to Superimposition
- BougĂ©, Francez
- 1988
(Show Context)
Citation Context ... the algorithm is reinvoked whenever no leader has been chosen. When n is known, a suitable distributed termination detection algorithm adapted to such situations can be superimposed on any algorithm =-=[BF]-=-. The technique to detect termination distributedly [SF] can be used by every processor individually to check whether all the other processors have halted. Incorrect termination can be replaced, there... |

33 |
A formal model for message passing systems
- Burns
- 1980
(Show Context)
Citation Context ...blem of choosing a leader is easier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader (=-=[Bu]-=-, [CR], [DKR], [F1], [HS], [L], [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has ... |

29 | On the existence of symmetric algorithms to find leaders in networks of communicating sequential processes - BougĂ© - 1988 |

23 |
The choice coordination problem
- Rabin
- 1982
(Show Context)
Citation Context ...assume that even though the processors are identical, each has an independent random number generator. (For a use of probabilistic algorithms for symmetry breaking in a shared memory environment, see =-=[R2]-=-.) Our theme is that to break symmetry one can develop a probabilistic routine to suggest and improve solutions together with a routine to test the correctness of the proposed solution. Obviously, we ... |

17 |
On an improved algorithm for decentralized extrema finding in circular configurations of processors
- Franklin
- 1982
(Show Context)
Citation Context ...leader is easier in asymlord - August 10, 1997 # # 2 metric networks. For example, if each processor has a unique id then the processor with the maximum id may serve as the leader ([Bu], [CR], [DKR], =-=[F1]-=-, [HS], [L], [Pe]). The problem of finding n, the size of the ring, is discussed in Section 4. This problem is directly related to that of termination. Usually when a processor has computed the requir... |

17 |
A new approach to detection of locally indicative stability
- Shavit, Francez
- 1986
(Show Context)
Citation Context ...chosen. When n is known, a suitable distributed termination detection algorithm adapted to such situations can be superimposed on any algorithm [BF]. The technique to detect termination distributedly =-=[SF]-=- can be used by every processor individually to check whether all the other processors have halted. Incorrect termination can be replaced, therefore, by reinvocation of the algorithm. Assume that A te... |

9 |
Two lower bounds in asynchronous distributed computation
- Duris, Galil
(Show Context)
Citation Context ...unds for asynchronous rings where n is known, and in rings where a good estimate for n exists. Their paper considered only message termination and considered the probability of error. Duris and Galil =-=[DG]-=- have shown a lower bound on the average time required for finding the maximum in a ring (the average is taken over all distributions of the input). Pachl [Pa] and Itai et al [IMN] give a lower bound ... |

7 |
On the bit complexity of distributed computation in a ring with a leader
- Mansour, Zaks
- 1986
(Show Context)
Citation Context ...n requires an additional O (nlogn) bits. A crossing sequence argument may be used to show that W(nlogn) is a lower bound on deterministic algorithms. (A formal proof may be given using the results of =-=[MZ]-=-). 4.4. A message terminating algorithm to find n with low probability of error In this section we present an asynchronous algorithm with the following properties: (i) It always processor terminates. ... |

6 |
Probabilistic solitude verification on a ring
- Abrahamson, Adler, et al.
- 1986
(Show Context)
Citation Context ...ms. This paper also contains an improved algorithm to choose a leader in an asynchronous ring (section 3.4) and an algorithm to find n when possible (section 4.3.1). Following [IR], Abrahamson et al. =-=[AAHK]-=- considered the subproblem of solitude verification -- verifying that there is only one live processor. They gave upper and lower bounds for asynchronous rings where n is known, and in rings where a g... |

5 |
private communication
- Lempel
- 1964
(Show Context)
Citation Context ...nd each phase requires n time slots. ## # 2.4. Better algorithms to choose a leader. In the above algorithm the processors only counted the number of candidates. Here we follow a suggestion of Lempel =-=[Lem]-=- and consider an algorithm which uses additional information available to the processors. This algorithm exhibits a tradeoff between time and communication complexity by introducing a parameter q know... |

3 |
A lower bound for probabilistic distributed algorithms
- Pachl
- 1987
(Show Context)
Citation Context ...he probability of error. Duris and Galil [DG] have shown a lower bound on the average time required for finding the maximum in a ring (the average is taken over all distributions of the input). Pachl =-=[Pa]-=- and Itai et al [IMN] give a lower bound over all randomized algorithms. 2. CHOOSING A LEADER IN A SYNCHRONOUS RING lord - August 10, 1997 # # 3 2.1. The Model A unidirectional ring consists of n proc... |