Lecture 11-cs648-2013 Randomized Algorithms
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This document discusses hashing techniques for achieving efficient search times. It covers hashing, collisions, why hashing works well in practice, achieving worst-case O(1) search time using universal hash families, and static hashing for worst-case O(1) search time. The document focuses on techniques for efficient searching using hashing and how universal hash families can formally capture the notion of hash functions spreading elements uniformly.
Lecture 11-cs648-2013 Randomized Algorithms
- 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.
- 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.