# Introduction to Distributed Algorithm Part One_ Protocols Chapter 2

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```					Introduction to Distributed Algorithm
Part Two: Fundamental Algorithm
Chapter 7- Election Algorithms

Teacher: Chun-Yuan Lin

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Election Algorithms (1)
n   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 ).
n   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 leader and all other processes are in the state lost.

n   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.

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

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Introduction (1)
n   The process in state leader at the end of the computation is called the
leader and is said to be elected by the algorithm.

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Introduction (2)

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Assumptions Made in this Chapter (1)
n   The election problem has been studied in this chapter under
assumptions that we now review

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Assumptions Made in this Chapter (2)

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Elections and Waves
n   Election with the tree algorithm (find smallest identity)

n   Election with the phase algorithm

n   Election with Finn's algorithm

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(leave to root)
(root to leave)

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Ring Networks (1)
n   In this section some election algorithms for unidirectional rings are
considered. The election problem was first posed for the context of
ring networks by LeLann (message complexity O(N2) ).

n   This solution was improved by Chang and Roberts (worst case
complexity O(N2), average case complexity O(NlogN)).

n   Hirschberg-Sinclair algorithm required channels to be bidirectional
(worst case complexity O(NlogN)).

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Ring Networks (2)
n   Petersen and Dolev, Klawe, and Rodeh independently proposed all
O(NlogN) solution for the unidirectional ring.

n   A worst case lower bound of 0.34N log N messages for bidirectional
rings was proved by Bodlaender.

n   Pachl, Korach, and Rotem proved lower bounds of Ω(NlogN) for the
average case complexity, both for bidirectional and unidirectional
rings.

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The Algorithms of LeLann and of
Chang and Roberts (1)
n   The Algorithms of LeLann

(more than one initiator)
(some are not initiator)
unidirectional rings

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The Algorithms of LeLann and of
Chang and Roberts (2)

n   The Algorithms of Chang and Roberts

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The Peterson/Dolev-Klawe-Rodeh
Algorithm

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(until only one active)

(not, send again)

unidirectional rings

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

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A Lower-bound Result (2)

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Arbitrary Networks

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Extinction and a Fast Algorithm
(1)

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Extinction and a
Fast Algorithm
(2)
(only one wave)

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The Gallager-Humblet-Spira Algorithm (1)

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The Gallager-Humblet-Spira Algorithm (2)

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Global Description of the GHS Algorithm (1)

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Global Description of the GHS Algorithm (2)

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Global Description of the GHS Algorithm (3)

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Detailed
Description
of the GHS
Algorithm
(1)

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Detailed
Description
of the GHS
Algorithm
(2)

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Detailed
Description of
the GHS
Algorithm (3)

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The Korach-Kutten-Nloran Algorithm

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Applications of the KKM Algorithm

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```
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