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Introduction to Distributed Algorithm Part Two: Fundamental Algorithm Chapter 7- Election Algorithms. Teacher: Chun-Yuan Lin. Election Algorithms (1).
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Introduction to Distributed AlgorithmPart Two: Fundamental AlgorithmChapter 7- Election Algorithms Teacher: Chun-Yuan Lin Election Algorithms
Election Algorithms (1) • In this chapter the problem of election, also called leader finding, will be discussed. The election problem was first posed by LeLann (Subsection 7.2.1 ). • The problem is to start from a configuration where all processes are in the same state, and arrive at a configuration where exactly one process is in state leaderand all other processes are in the state lost. • An election under the processes must be held if a centralized algorithm is to be executed and there is no a priori candidate to serve as the initiator of this algorithm. Election Algorithms
Election Algorithms (2) • A large number of results about the election problem exist. Election Algorithms
Introduction (1) • The process in state leaderat the end of the computation is called the leader and is said to be elected by the algorithm. Election Algorithms
Introduction (2) Election Algorithms
Assumptions Made in this Chapter (1) • The election problem has been studied in this chapter under assumptions that we now review Election Algorithms
Assumptions Made in this Chapter (2) Election Algorithms
Elections and Waves • Election with the tree algorithm (find smallest identity) • Election with the phase algorithm • Election with Finn's algorithm Election Algorithms
(leave to root) (root to leave) Election Algorithms
Ring Networks (1) • In this section some election algorithms for unidirectionalrings are considered. The election problem was first posed for the context of ring networks by LeLann (message complexity O(N2) ). • This solution was improved by Chang and Roberts (worst case complexity O(N2), average case complexity O(NlogN)). • Hirschberg-Sinclair algorithm required channels to be bidirectional (worst casecomplexity O(NlogN)). Election Algorithms
Ring Networks (2) • Petersen and Dolev, Klawe, and Rodeh independently proposed all O(NlogN) solution for the unidirectional ring. • A worst case lower bound of 0.34N log N messages for bidirectional rings was proved by Bodlaender. • Pachl, Korach, and Rotem proved lower bounds of Ω(NlogN) for the average case complexity, both for bidirectional and unidirectional rings. Election Algorithms
The Algorithms of LeLann and of Chang and Roberts (1) • The Algorithms of LeLann (more than one initiator) (some are not initiator) (receive all tok) unidirectionalrings Election Algorithms
The Algorithms of LeLann and of Chang and Roberts (2) • The Algorithms of Chang and Roberts Election Algorithms
unidirectionalrings Election Algorithms (only pass better tok)
The Peterson/Dolev-Klawe-Rodeh Algorithm Election Algorithms
(until only one active) (not, send again) unidirectionalrings Election Algorithms
A Lower-bound Result (1) • The result is due to Pachl, Korach, and Rotem and is obtained under the following assumptions. Election Algorithms
A Lower-bound Result (2) Election Algorithms
Arbitrary Networks Election Algorithms
Extinction and a Fast Algorithm (1) Election Algorithms
Extinction and a Fast Algorithm (2) (only one wave) Election Algorithms
The Gallager-Humblet-Spira Algorithm (1) Election Algorithms
The Gallager-Humblet-Spira Algorithm (2) Election Algorithms
Global Description of the GHS Algorithm (1) Election Algorithms
Global Description of the GHS Algorithm (2) Election Algorithms
Global Description of the GHS Algorithm (3) Election Algorithms
Detailed Description of the GHS Algorithm (1) Election Algorithms
Detailed Description of the GHS Algorithm (2) Election Algorithms
Detailed Description of the GHS Algorithm (3) Election Algorithms
The Korach-Kutten-Nloran Algorithm Election Algorithms
Applications of the KKM Algorithm Election Algorithms