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CS 245: Database System Principles

CS 245: Database System Principles. Notes 5: Hashing and More. Hector Garcia-Molina. Hashing. key  h(key). <key>. Buckets (typically 1 disk block). Two alternatives. records. (1) key  h(key). Two alternatives. record. (2) key  h(key). key 1. Index. Two alternatives.

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CS 245: Database System Principles

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  1. CS 245: Database System Principles Notes 5: Hashing and More Hector Garcia-Molina Notes 5

  2. Hashing key  h(key) <key> Buckets (typically 1 disk block) . . . Notes 5

  3. Two alternatives . . . records (1) key  h(key) . . . Notes 5

  4. Two alternatives record (2) key  h(key) key 1 Index Notes 5

  5. Two alternatives record (2) key  h(key) key 1 Index • Alt (2) for “secondary” search key Notes 5

  6. Example hash function • Key = ‘x1 x2 … xn’ n byte character string • Have b buckets • h: add x1 + x2 + ….. xn • compute sum modulo b Notes 5

  7.  This may not be best function …  Read Knuth Vol. 3 if you really need to select a good function. Notes 5

  8.  This may not be best function …  Read Knuth Vol. 3 if you really need to select a good function. Good hash  Expected number of function: keys/bucket is the same for all buckets Notes 5

  9. Within a bucket: • Do we keep keys sorted? • Yes, if CPU time critical • & Inserts/Deletes not too frequent Notes 5

  10. Next: example to illustrate inserts, overflows, deletes h(K) Notes 5

  11. EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = 0 0 1 2 3 Notes 5

  12. d a c b EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = 0 0 1 2 3 h(e) = 1 Notes 5

  13. d a e c b EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = 0 0 1 2 3 h(e) = 1 Notes 5

  14. EXAMPLE: deletion Delete:ef 0 1 2 3 a b d c e f g Notes 5

  15. maybe move “g” up EXAMPLE: deletion Delete:ef 0 1 2 3 a b d c c e f g Notes 5

  16. d maybe move “g” up EXAMPLE: deletion Delete:ef 0 1 2 3 a b d c c e f g Notes 5

  17. Rule of thumb: • Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit Notes 5

  18. If < 50%, wasting space • If > 80%, overflows significant depends on how good hash function is & on # keys/bucket Rule of thumb: • Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit Notes 5

  19. How do we cope with growth? • Overflows and reorganizations • Dynamic hashing Notes 5

  20. Extensible • Linear How do we cope with growth? • Overflows and reorganizations • Dynamic hashing Notes 5

  21. Extensible hashing: two ideas (a) Use i of b bits output by hash function b h(K)  use i grows over time…. 00110101 Notes 5

  22. (b) Use directory h(K)[i ] to bucket . . . . . . Notes 5

  23. 1 Example: h(k) is 4 bits; 2 keys/bucket 1 0001 i = 1 1001 1100 Insert 1010 Notes 5

  24. 1 1 1010 1100 Example: h(k) is 4 bits; 2 keys/bucket 1 0001 i = 1 1001 1100 Insert 1010 Notes 5

  25. i = 2 00 01 10 11 1 1 2 1010 New directory 2 1100 Example: h(k) is 4 bits; 2 keys/bucket 1 0001 i = 1 1001 1100 Insert 1010 Notes 5

  26. 2 2 Example continued i = 2 00 01 10 11 1 0001 1001 1010 Insert: 0111 0000 1100 Notes 5

  27. 0000 0001 0111 2 2 Example continued i = 2 00 01 10 11 1 0001 0111 1001 1010 Insert: 0111 0000 1100 Notes 5

  28. 2 0000 0001 2 0111 2 2 Example continued i = 2 00 01 10 11 1 0001 0111 1001 1010 Insert: 0111 0000 1100 Notes 5

  29. 1001 2 1010 1100 2 Example continued 0000 2 0001 i = 2 00 01 10 11 0111 2 Insert: 1001 Notes 5

  30. 1001 1001 2 1001 1010 1010 1100 2 Example continued 0000 2 0001 i = 2 00 01 10 11 0111 2 Insert: 1001 Notes 5

  31. i = 3 000 001 010 011 100 101 110 111 3 1001 1001 2 1001 1010 3 1010 1100 2 Example continued 0000 2 0001 i = 2 00 01 10 11 0111 2 Insert: 1001 Notes 5

  32. Extensible hashing: deletion • No merging of blocks • Merge blocks and cut directory if possible (Reverse insert procedure) Notes 5

  33. Deletion example: • Run thru insert example in reverse! Notes 5

  34. 1 2 2 Note: Still need overflow chains • Example: many records with duplicate keys if we split: insert 1100 1101 1100 1100 1100 Notes 5

  35. 1 1 Solution: overflow chains add overflow block: insert 1100 1100 1101 1101 1101 1100 Notes 5

  36. Summary Extensible hashing + Can handle growing files - with less wasted space - with no full reorganizations Notes 5

  37. Indirection (Not bad if directory in memory) Directory doubles in size (Now it fits, now it does not) - - Summary Extensible hashing + Can handle growing files - with less wasted space - with no full reorganizations Notes 5

  38. Two ideas: b (a) Use ilow order bits of hash 01110101 grows i Linear hashing • Another dynamic hashing scheme Notes 5

  39. Two ideas: b (a) Use ilow order bits of hash 01110101 grows i (b) File grows linearly Linear hashing • Another dynamic hashing scheme Notes 5

  40. Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  41. If h(k)[i ]  m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ]- 2i -1 Rule Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  42. If h(k)[i ]  m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ]- 2i -1 Rule Exampleb=4 bits, i =2, 2 keys/bucket • insert 0101 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  43. 0101 • can have overflow chains! If h(k)[i ]  m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ]- 2i -1 Rule Exampleb=4 bits, i =2, 2 keys/bucket • insert 0101 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  44. Note • In textbook, n is used instead of m • n=m+1 n=10 Future growth buckets 0000 0101 1010 1111 00 01 10 11 m = 01 (max used block) Notes 5

  45. Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  46. 1010 10 Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  47. 0101 • insert 0101 1010 10 Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  48. 0101 • insert 0101 1010 10 11 Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  49. 0101 • insert 0101 1010 1111 0101 10 11 Exampleb=4 bits, i =2, 2 keys/bucket 00 01 10 11 Future growth buckets 0000 0101 1010 1111 m = 01 (max used block) Notes 5

  50. Example Continued:How to grow beyond this? i = 2 00 01 10 11 0000 0101 1010 1111 0101 . . . m = 11 (max used block) Notes 5

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