נושאים מתקדמים באלגוריתמים מבוזרים

שמואל זקסzaks@cs.technion.ac.il, www.cs.technion.ac.il/~zaks

A. Distributed algorithms

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8 days, 1 professor 4 days, 2 professorExercise: find a trade-off between no. of

days and no. of professors.

Example 1: synchony9

9

4

5

8

6

Example 2: leader election

?

x

x x

xExercise: find a better algorithm to find the

maximum, prove correctness and analyze performance.

Example 3: faults

Impossibility of consensus

The Byzantine Generals Problem

Example 4: snapshot

Example 5: self stabilization

6 6

6

6

6

7

7

7

7

7

B. Self Stabilization

6 7

6

4 6

Exercise: find an algorithm to do it, prove correctness, analyze performance.

:3-ממדי ברדיוס 2כדור

C. Networks (optical)

sp(2,3)= 25

Example 6: layout

-ממדי ברדיוס 2כדור

1 2-ממדי ברדיוס 1כדור

sp(2,1)= sp(1,2)= 5

Exercise: prove: sp(x,y)= sp(y,x)

lightpaths

p1

p2

1 2( ) ( )w p w p

Valid coloring

Example 7: switching cost (approximation, on-line algs)

Saving a switch:

colors = 2

switches = 8

colors=3

switches = 7

colors=3 switches=10

colors=2 switches=9

g=2w/ grooming

Complexity issues (NP-complete vs P) Approximation algorithms On-line algorithms Various cost measures