Teacher: Chun-Yuan Lin

1. Introduction to Distributed AlgorithmPart Two: Fundamental AlgorithmChapter 7- Election Algorithms Teacher: Chun-Yuan Lin Election Algorithms

2. 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

3. Election Algorithms (2) • A large number of results about the election problem exist. Election Algorithms

4. 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

5. Introduction (2) Election Algorithms

6. Assumptions Made in this Chapter (1) • The election problem has been studied in this chapter under assumptions that we now review Election Algorithms

7. Assumptions Made in this Chapter (2) Election Algorithms

8. Elections and Waves • Election with the tree algorithm (find smallest identity) • Election with the phase algorithm • Election with Finn's algorithm Election Algorithms

9. (leave to root) (root to leave) Election Algorithms

10. 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

11. 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

12. 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

13. The Algorithms of LeLann and of Chang and Roberts (2) • The Algorithms of Chang and Roberts Election Algorithms

14. unidirectionalrings Election Algorithms (only pass better tok)

15. The Peterson/Dolev-Klawe-Rodeh Algorithm Election Algorithms

16. (until only one active) (not, send again) unidirectionalrings Election Algorithms

17. A Lower-bound Result (1) • The result is due to Pachl, Korach, and Rotem and is obtained under the following assumptions. Election Algorithms

18. A Lower-bound Result (2) Election Algorithms

19. Arbitrary Networks Election Algorithms

20. Extinction and a Fast Algorithm (1) Election Algorithms

21. Extinction and a Fast Algorithm (2) (only one wave) Election Algorithms

22. The Gallager-Humblet-Spira Algorithm (1) Election Algorithms

23. The Gallager-Humblet-Spira Algorithm (2) Election Algorithms

24. Global Description of the GHS Algorithm (1) Election Algorithms

25. Global Description of the GHS Algorithm (2) Election Algorithms

26. Global Description of the GHS Algorithm (3) Election Algorithms

27. Detailed Description of the GHS Algorithm (1) Election Algorithms

28. Detailed Description of the GHS Algorithm (2) Election Algorithms

29. Detailed Description of the GHS Algorithm (3) Election Algorithms

30. The Korach-Kutten-Nloran Algorithm Election Algorithms

31. Election Algorithms

32. Applications of the KKM Algorithm Election Algorithms