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נושאים מתקדמים באלגוריתמים מבוזרים. שמואל זקס [email protected] , www.cs.technion.ac.il/~zaks. A. Distributed algorithms. Example 1: synchony. 9. 8. 7. 6. 5. 4. 3. 2. 1. 8 days, 1 professor. 4 days, 2 professor. - PowerPoint PPT Presentation
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נושאים מתקדמים באלגוריתמים מבוזרים
שמואל זקס[email protected], www.cs.technion.ac.il/~zaks
A. Distributed algorithms
12345678
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