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Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
Lecture 11-cs648-2013 Randomized Algorithms
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Lecture 11-cs648-2013 Randomized Algorithms

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  • 1. Randomized Algorithms CS648 Lecture 11 Hashing - I 1
  • 2. Problem Definition
  • 3. Solutions
  • 4. Hashing
  • 5. Collision
  • 6. Collision
  • 7. Hashing
  • 8. WHY DOES HASHING WORK SO WELL IN PRACTICE ?
  • 9. Why does hashing work so well in Practice ?
  • 10. Why does hashing work so well in Practice ? 1 2 m
  • 11. Why does hashing work so well in Practice ? 1 2 m
  • 12. Why does hashing work so well in Practice ?
  • 13. HOW TO ACHIEVE WORST CASE O(1) SEARCH TIME
  • 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. UNIVERSAL HASH FAMILY
  • 16. Universal Hash Family
  • 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. STATIC HASHING WORST CASE O(1) SEARCH TIME
  • 19. The Journey
  • 20. Use Markov’s Inequality to bound it.

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