1. Randomized Algorithms
CS648
Lecture 18
• Approximate Distance Oracles
• Algorithm for Min-cut : part 1
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2. APPROXIMATE DISTANCE ORACLES
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3. All-Pairs Shortest Paths
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4. All-Pairs Shortest Paths
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5. All-Pairs Approximate Shortest Paths
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6. A truly magical result
Approximate Distance Oracles
Space
Query time
Preprocessing time
Mikkel Thorup and Uri Zwick:
Approximate Distance Oracles for graphs,
Journal of ACM (4), 2005
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7. INSPIRATION FROM
OUR DAILY LIFE
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8. Air/Road Network
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9. The Idea
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10. Formal notion of locality
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11. Formal notion of locality
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12. 12

13. What is the stretch ?
??
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14. 3-approximate distance oracle
Global distance info.
Local distance info.
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15. The real challenge left
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16. The real challenge left
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17. Conquering the challenge
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18. 18

19. Expected space of
3-approximate distance oracle
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20. 20

21. 5-APPROXIMATE DISTANCE ORACLE
Meant for only those (hopefully nonzero no. of) students whose aim is
more than just a good grade in this course.
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22. 3-approximate distance oracle
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23. 5-approximate distance oracle
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24. 5-approximate distance oracle
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25. PROBLEM 2
MIN-CUT
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26. Min-Cut
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27. Min-Cut
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28. SOME BASIC FACTS
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29. Min-Cut
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30. 30

31. 31

32. 32

33. 33

34. Algorithm for min-cut
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35. Algorithm for min-cut
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36. Algorithm for min-cut
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