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נושאים מתקדמים באלגוריתמים מבוזרים

נושאים מתקדמים באלגוריתמים מבוזרים. שמואל זקס zaks@cs.technion.ac.il , 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 .

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נושאים מתקדמים באלגוריתמים מבוזרים

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  1. נושאים מתקדמים באלגוריתמים מבוזרים שמואל זקס zaks@cs.technion.ac.il, www.cs.technion.ac.il/~zaks

  2. A. Distributed algorithms Example 1: synchony 9 8 7 6 5 4 3 2 1 8 days, 1 professor 4 days, 2 professor Exercise: find a trade-off between no. of days and no. of professors.

  3. Example 2: leader election x x 4 8 ? x x 5 6 9 Exercise: find a better algorithm to find the maximum, prove correctness and analyze performance.

  4. Example 3: faults Impossibility of consensusThe Byzantine Generals Problem

  5. Example 4: snapshot

  6. B. Self Stabilization Example 5: self stabilization 6 7 6 7 6 7 6 7 6 7

  7. 6 7 6 6 4 Exercise: find an algorithm to do it, prove correctness, analyze performance.

  8. C. Networks (optical) כדור 2-ממדי ברדיוס 3: Example 6: layout sp(2,3)= 25

  9. כדור 2-ממדי ברדיוס 1 כדור 1-ממדי ברדיוס 2 sp(2,1)= sp(1,2)= 5 Exercise: prove: sp(x,y)= sp(y,x)

  10. Example 7: switching cost (approximation, on-line algs) lightpaths Valid coloring p1 p2

  11. Saving a switch:

  12. colors=3 switches = 7 colors = 2 switches = 8

  13. w/ grooming g=2 colors=3 switches=10 colors=2 switches=9

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

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