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When a randomized algorithm elects a leader on anonymous networks, initial information (which is called in general *initial condition* in this paper) of some sort is always needed. In this paper, we study common properties of initial conditions that enable a randomized algorithm to elect a leader. In the previous papers, the author introduced the notion of transformation between initial conditions using distributed algorithms. By using this notion of transformation, we investigate the property of initial conditions for the leader election. We define that an initial condition *C* is *p*(*N*)-complete if there exists some randomized algorithm that elects a leader with probability *p*(*N*) on any size *N* network satisfying *C*. We show that we can divide *p*(*N*)-completeness into four types as follows. 1. *p*(*N*)=1: For any 1-complete initial conditions, there exists a deterministic distributed algorithm that can compute the size of the network for any initial information satisfying the initial condition. 2. inf *p*(*N*) >0: For any *p*(*N*)-complete initial conditions with inf *p*(*N*) >0, there exists a deterministic distributed algorithm that can compute an upper-bound for the size of the network for any initial information satisfying the initial condition. 3. inf *p*(*N*) converges to 0: The set of *p*(*N*)-complete initial conditions varies depending on the decrease rate of *p*(*N*). 4. *p*(*N*) decreases exponentially: Any initial condition is regarded as *p*(*N*)-complete.

- Publication
- IEICE TRANSACTIONS on Information Vol.E85-D No.1 pp.203-213

- Publication Date
- 2002/01/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- PAPER

- Category
- Algorithms

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Naoshi SAKAMOTO, "Initial Conditions Solving the Leader Election Problem by Randomized Algorithms" in IEICE TRANSACTIONS on Information,
vol. E85-D, no. 1, pp. 203-213, January 2002, doi: .

Abstract: When a randomized algorithm elects a leader on anonymous networks, initial information (which is called in general *initial condition* in this paper) of some sort is always needed. In this paper, we study common properties of initial conditions that enable a randomized algorithm to elect a leader. In the previous papers, the author introduced the notion of transformation between initial conditions using distributed algorithms. By using this notion of transformation, we investigate the property of initial conditions for the leader election. We define that an initial condition *C* is *p*(*N*)-complete if there exists some randomized algorithm that elects a leader with probability *p*(*N*) on any size *N* network satisfying *C*. We show that we can divide *p*(*N*)-completeness into four types as follows. 1. *p*(*N*)=1: For any 1-complete initial conditions, there exists a deterministic distributed algorithm that can compute the size of the network for any initial information satisfying the initial condition. 2. inf *p*(*N*) >0: For any *p*(*N*)-complete initial conditions with inf *p*(*N*) >0, there exists a deterministic distributed algorithm that can compute an upper-bound for the size of the network for any initial information satisfying the initial condition. 3. inf *p*(*N*) converges to 0: The set of *p*(*N*)-complete initial conditions varies depending on the decrease rate of *p*(*N*). 4. *p*(*N*) decreases exponentially: Any initial condition is regarded as *p*(*N*)-complete.

URL: https://global.ieice.org/en_transactions/information/10.1587/e85-d_1_203/_p

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@ARTICLE{e85-d_1_203,

author={Naoshi SAKAMOTO, },

journal={IEICE TRANSACTIONS on Information},

title={Initial Conditions Solving the Leader Election Problem by Randomized Algorithms},

year={2002},

volume={E85-D},

number={1},

pages={203-213},

abstract={When a randomized algorithm elects a leader on anonymous networks, initial information (which is called in general *initial condition* in this paper) of some sort is always needed. In this paper, we study common properties of initial conditions that enable a randomized algorithm to elect a leader. In the previous papers, the author introduced the notion of transformation between initial conditions using distributed algorithms. By using this notion of transformation, we investigate the property of initial conditions for the leader election. We define that an initial condition *C* is *p*(*N*)-complete if there exists some randomized algorithm that elects a leader with probability *p*(*N*) on any size *N* network satisfying *C*. We show that we can divide *p*(*N*)-completeness into four types as follows. 1. *p*(*N*)=1: For any 1-complete initial conditions, there exists a deterministic distributed algorithm that can compute the size of the network for any initial information satisfying the initial condition. 2. inf *p*(*N*) >0: For any *p*(*N*)-complete initial conditions with inf *p*(*N*) >0, there exists a deterministic distributed algorithm that can compute an upper-bound for the size of the network for any initial information satisfying the initial condition. 3. inf *p*(*N*) converges to 0: The set of *p*(*N*)-complete initial conditions varies depending on the decrease rate of *p*(*N*). 4. *p*(*N*) decreases exponentially: Any initial condition is regarded as *p*(*N*)-complete.},

keywords={},

doi={},

ISSN={},

month={January},}

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TY - JOUR

TI - Initial Conditions Solving the Leader Election Problem by Randomized Algorithms

T2 - IEICE TRANSACTIONS on Information

SP - 203

EP - 213

AU - Naoshi SAKAMOTO

PY - 2002

DO -

JO - IEICE TRANSACTIONS on Information

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VL - E85-D

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JA - IEICE TRANSACTIONS on Information

Y1 - January 2002

AB - When a randomized algorithm elects a leader on anonymous networks, initial information (which is called in general *initial condition* in this paper) of some sort is always needed. In this paper, we study common properties of initial conditions that enable a randomized algorithm to elect a leader. In the previous papers, the author introduced the notion of transformation between initial conditions using distributed algorithms. By using this notion of transformation, we investigate the property of initial conditions for the leader election. We define that an initial condition *C* is *p*(*N*)-complete if there exists some randomized algorithm that elects a leader with probability *p*(*N*) on any size *N* network satisfying *C*. We show that we can divide *p*(*N*)-completeness into four types as follows. 1. *p*(*N*)=1: For any 1-complete initial conditions, there exists a deterministic distributed algorithm that can compute the size of the network for any initial information satisfying the initial condition. 2. inf *p*(*N*) >0: For any *p*(*N*)-complete initial conditions with inf *p*(*N*) >0, there exists a deterministic distributed algorithm that can compute an upper-bound for the size of the network for any initial information satisfying the initial condition. 3. inf *p*(*N*) converges to 0: The set of *p*(*N*)-complete initial conditions varies depending on the decrease rate of *p*(*N*). 4. *p*(*N*) decreases exponentially: Any initial condition is regarded as *p*(*N*)-complete.

ER -