### Abstract

The leader election problem is unsolvable for some anonymous networks. A leader election algorithm for anonymous networks thus elects a leader whenever it is possible; if it is impossible, the algorithm reports this fact. This paper investigates the space complexity of the leader election problem in anonymous networks, where the space complexity is measured by the size (in the number of bits) of memory per processor used by a leader election algorithm. We first observe that Ω(M + log d) bits are necessary and then show that O(n log d) bits are sufficient to construct a leader election algorithm that works on any network, where n, d and M are the number of processors, the maximum number of adjacent processors, and the maximum size (in bits) of a message, respectively. We next show that, for any arbitrarily fixed constant n, O(1) bits are sufficient to construct a leader election algorithm that works in any network of size n.

Original language | English |
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Pages (from-to) | 427-440 |

Number of pages | 14 |

Journal | International Journal of Foundations of Computer Science |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)

### Cite this

*International Journal of Foundations of Computer Science*,

*21*(3), 427-440. https://doi.org/10.1142/S0129054110007349

**The space complexity of leader election in anonymous networks.** / Ando, E. I.; Ono, Hirotaka; Sadakane, Kunihiko; Yamashita, Masafumi.

Research output: Contribution to journal › Article

*International Journal of Foundations of Computer Science*, vol. 21, no. 3, pp. 427-440. https://doi.org/10.1142/S0129054110007349

}

TY - JOUR

T1 - The space complexity of leader election in anonymous networks

AU - Ando, E. I.

AU - Ono, Hirotaka

AU - Sadakane, Kunihiko

AU - Yamashita, Masafumi

PY - 2010/6/1

Y1 - 2010/6/1

N2 - The leader election problem is unsolvable for some anonymous networks. A leader election algorithm for anonymous networks thus elects a leader whenever it is possible; if it is impossible, the algorithm reports this fact. This paper investigates the space complexity of the leader election problem in anonymous networks, where the space complexity is measured by the size (in the number of bits) of memory per processor used by a leader election algorithm. We first observe that Ω(M + log d) bits are necessary and then show that O(n log d) bits are sufficient to construct a leader election algorithm that works on any network, where n, d and M are the number of processors, the maximum number of adjacent processors, and the maximum size (in bits) of a message, respectively. We next show that, for any arbitrarily fixed constant n, O(1) bits are sufficient to construct a leader election algorithm that works in any network of size n.

AB - The leader election problem is unsolvable for some anonymous networks. A leader election algorithm for anonymous networks thus elects a leader whenever it is possible; if it is impossible, the algorithm reports this fact. This paper investigates the space complexity of the leader election problem in anonymous networks, where the space complexity is measured by the size (in the number of bits) of memory per processor used by a leader election algorithm. We first observe that Ω(M + log d) bits are necessary and then show that O(n log d) bits are sufficient to construct a leader election algorithm that works on any network, where n, d and M are the number of processors, the maximum number of adjacent processors, and the maximum size (in bits) of a message, respectively. We next show that, for any arbitrarily fixed constant n, O(1) bits are sufficient to construct a leader election algorithm that works in any network of size n.

UR - http://www.scopus.com/inward/record.url?scp=77953532223&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953532223&partnerID=8YFLogxK

U2 - 10.1142/S0129054110007349

DO - 10.1142/S0129054110007349

M3 - Article

AN - SCOPUS:77953532223

VL - 21

SP - 427

EP - 440

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 3

ER -