1. Cache-Oblivious Algorithms By Ofer Freedman

2. The Real World • In Theory • LCS problem • Analysis

3. 1. The Real World

4. חומרה

6. Cache Miss

7. Page Fault

8. I/O Bound

9. Latency

10. 2. In Theory

11. RAM model

12. all memories are equal

13. all memories are equal But some more than Others

14. standard external-memory model AlokAggarwal and Jeff Vitter, 1988

15. Storage > ∞ M – finite memory B – block size

16. Analysis

17. Time Complexity

18. Space Complexity

19. Cache Complexity

20. We want to bound number of cache misses

21. Some results: Scanning: Binary Search: Sort:

22. In B-trees: B = B

23. Many Problems

24. 1. Requires tuning for every machine.

25. 2. The OS might not tell us what we need to know.

26. 3. How do we optimize for multi level cache?

27. Cache-Oblivious Model Frigo, Leiserson, Prokop, and Ramachandran, 1999

28. Storage > ∞ M – finite memory B – block size

29. With the following additions

30. Algorithm may not know about B and M.

31. Algorithm have no control over blocks placing

32. B and M apply only in analysis.

33. Why is it Great?

34. 1. Require no tuning.

35. 2. RAM is cache-oblivious out of the box.

36. 3. Optimal for multi-level cache hierarchy

37. CPU RAM L2Cache L1Cache

38. Memory Storage CPU RAM L2Cache L1Cache

39. Memory Storage CPU RAM L2Cache L1Cache

40. Memory Storage CPU RAM L2Cache L1Cache

41. What about cache management policy?

42. Good News

43. (double) optimal policy (with M memory) FIFO and LRU (with 2M cache)

44. 3. LCS

45. Input: 2 strings X and Y,of length n and m.

46. Output: Longest Common Subsequence of X and Y

47. HUMAN CHIMPANZEE

48. HUMAN CHIMPANZEE

49. Naive Solution