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

22. Use Markov’s Inequality to
bound it.