Lecture 11-cs648-2013 Randomized Algorithms

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Lecture 11-cs648-2013 Randomized Algorithms

  1. 1. Randomized Algorithms CS648 Lecture 11 Hashing - I 1
  2. 2. Problem Definition
  3. 3. Solutions
  4. 4. Hashing
  5. 5. Collision
  6. 6. Collision
  7. 7. Hashing
  8. 8. WHY DOES HASHING WORK SO WELL IN PRACTICE ?
  9. 9. Why does hashing work so well in Practice ?
  10. 10. Why does hashing work so well in Practice ? 1 2 m
  11. 11. Why does hashing work so well in Practice ? 1 2 m
  12. 12. Why does hashing work so well in Practice ?
  13. 13. HOW TO ACHIEVE WORST CASE O(1) SEARCH TIME
  14. 14. Key idea to achieve worst case O(1) search time The notion of goodness is captured formally by Universal hash family in the following slide.
  15. 15. UNIVERSAL HASH FAMILY
  16. 16. Universal Hash Family
  17. 17. Universal Hash Family This looks complicated. In the next class we shall show that it is very natural and intuitive. For today’s lecture, you don’t need it 
  18. 18. STATIC HASHING WORST CASE O(1) SEARCH TIME
  19. 19. The Journey
  20. 20. Use Markov’s Inequality to bound it.

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