scholarly journals A probabilistic analysis of a leader election algorithm

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Hanene Mohamed
Keyword(s):  
Asymptotic Behavior ◽  
Probabilistic Analysis ◽  
Probabilistic Approach ◽  
Leader Election ◽  
Hitting Time ◽  
Elimination Process ◽  
International Audience ◽  
Election Algorithm ◽  
The Cost ◽  
Leader Election Algorithm

International audience A leader election algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the cost of the algorithm e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1].

scholarly journals The asymmetric leader election algorithm with Swedish stopping: a probabilistic analysis

2012 ◽  
Vol Vol. 14 no. 2 (Analysis of Algorithms) ◽  
Author(s):  
Guy Louchard ◽  
Helmut Prodinger
Keyword(s):  
Mellin Transform ◽  
Analysis Of Algorithms ◽  
Early Stage ◽  
Success Probability ◽  
Companion Paper ◽  
Leader Election ◽  
International Audience ◽  
Election Algorithm ◽  
Probability Number ◽  
Leader Election Algorithm

Analysis of Algorithms International audience We study a leader election protocol that we call the Swedish leader election protocol. This name comes from a protocol presented by L. Bondesson, T. Nilsson, and G. Wikstrand (2007). The goal is to select one among n > 0 players, by proceeding through a number of rounds. If there is only one player remaining, the protocol stops and the player is declared the leader. Otherwise, all remaining players flip a biased coin; with probability q the player survives to the next round, with probability p = 1 - q the player loses (is killed) and plays no further ... unless all players lose in a given round (null round), so all of them play again. In the classical leader election protocol, any number of null rounds may take place, and with probability 1 some player will ultimately be elected. In the Swedish leader election protocol there is a maximum number tau of consecutive null rounds, and if the threshold is attained the protocol fails without declaring a leader. In this paper, several parameters are asymptotically analyzed, among them: Success Probability, Number of rounds R-n, Number of null rounds T-n. This paper is a companion paper to Louchard, Martinez and Prodinger (2011) where De-Poissonization was used, together with the Mellin transform. While this works fine as far as it goes, there are limitations, in particular of a computational nature. The approach chosen here is similar to earlier efforts of the same authors - Louchard and Prodinger (2004,2005,2009). Identifying some underlying distributions as Gumbel (type) distributions, one can start with approximations at a very early stage and compute (at least in principle) all moments asymptotically. This is in contrast to the companion work, where only expected values were considered. In an appendix, it is shown that, whereever results are given in both papers, they coincide, although they are presented in different ways.

scholarly journals Convergence of some leader election algorithms

2008 ◽  
Vol Vol. 10 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Svante Janson ◽  
Christian Lavault ◽  
Guy Louchard
Keyword(s):  
Probability Distributions ◽  
Random Variable ◽  
Wasserstein Distance ◽  
Leader Election ◽  
Stochastic Monotonicity ◽  
Fixed Proportion ◽  
Variation Distance ◽  
International Audience ◽  
Election Algorithm ◽  
Leader Election Algorithm

International audience We start with a set of $n$ players. With some probability $P(n,k)$, we kill $n-k$ players; the other ones stay alive, and we repeat with them. What is the distribution of the number $X_n$ of \emph{phases} (or rounds) before getting only one player? We present a probabilistic analysis of this algorithm under some conditions on the probability distributions $P(n,k)$, including stochastic monotonicity and the assumption that roughly a fixed proportion $\al$ of the players survive in each round. We prove a kind of convergence in distribution for $X_n - \log_{1/\!\alpha}(n)$; as in many other similar problems there are oscillations and no true limit distribution, but suitable subsequences converge, and there is an absolutely continuous random variable $Z$ such that $d\l(X_n, \lceil Z + \log_{1/\!\alpha} (n)\rceil\r) \to 0$, where $d$ is either the total variation distance or the Wasserstein distance. Applications of the general result include the leader election algorithm where players are eliminated by independent coin tosses and a variation of the leader election algorithm proposed by W.R. Franklin. We study the latter algorithm further, including numerical results.

A Novel Hypergraph-Based Leader Election Algorithm for Distributed Systems

2020 ◽  
pp. 437-445
Author(s):  
E. R. S. Subramanian ◽  
B. Sri Gurubaran ◽  
A. S. Sayee Shruthi ◽  
V. Aishwarya ◽  
N. Balaji ◽  
...  
Keyword(s):  
Distributed Systems ◽  
Leader Election ◽  
Election Algorithm ◽  
Leader Election Algorithm

Implementing Leader Election Algorithm after Evaluation of Node Trust in MANETs

2017 ◽  
pp. 282-311
Author(s):  
Jayanta Das ◽  
Abhijit Das
Keyword(s):  
Leader Election ◽  
Election Algorithm ◽  
Leader Election Algorithm

Security and trust are two inevitable concepts for secure Manet. There are various systems used for ensuring security and trust in case of Manet. These systems have several advantages as well as several disadvantages in terms high communication and computation overhead. In this proposed trust based system, trust of node is evaluated on the basis of ratio of signal sent and acknowledgement received. After that, priority of each node is calculated and at last Leader Election algorithm is applied to select node leader.

The Asymmetric Leader Election Algorithm: Another Approach

2009 ◽  
Vol 12 (4) ◽  
pp. 449-478 ◽  
Author(s):  
Guy Louchard ◽  
Helmut Prodinger
Keyword(s):  
Leader Election ◽  
Election Algorithm ◽  
Leader Election Algorithm

Optimal asynchronous agreement and leader election algorithm for complete networks with Byzantine faulty links

1995 ◽  
Vol 9 (3) ◽  
pp. 147-156 ◽  
Author(s):  
Hasan M. Sayeed ◽  
Marwan Abu-Amara ◽  
Hosame Abu-Amara
Keyword(s):  
Leader Election ◽  
Complete Networks ◽  
Election Algorithm ◽  
Leader Election Algorithm

Predictable Leader Election Algorithm

1995 ◽  
Vol 3 (3) ◽  
pp. 195-201
Author(s):  
Tai Woo Kim ◽  
Tai Yun Kim
Keyword(s):  
Leader Election ◽  
Election Algorithm ◽  
Leader Election Algorithm
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