1. Database Management Systems, R. Ramakrishnan and J. Gehrke 1 External Sorting Chapter 13

2. Database Management Systems, R. Ramakrishnan and J. Gehrke 2 Why Sort? v A classic problem in computer science! v Data requested in sorted order – e.g., find students in increasing gpa order – Nearest neighbor search also needs sorting! v Sorting is the first step in bulk loading B+ tree index. v Sorting useful for eliminating duplicate copies in a collection of records (Why?) v Sort-merge join algorithm involves sorting.

3. Database Management Systems, R. Ramakrishnan and J. Gehrke 3 Sorting Types v In-Memory Sorting : When the size of memory is bigger than that of file to be sorted! v External Sorting : When the size of file to be sorted is bigger than that of available memory!

4. Database Management Systems, R. Ramakrishnan and J. Gehrke 4 In-Memory Sorting: Heap-Sorting 4 1 3 2 16 9 10 14 8 7 Original Data Page 16 14 10 9 8 7 4 3 2 1 Sorted Data Page How can we obtain the sorted data page? 1.Build-Heap Procedure 2.Heapsort Procedure

5. Database Management Systems, R. Ramakrishnan and J. Gehrke 5 In-Memory Sorting: Heap-Sorting v Build-Heap Procedure 4 1 3 2 16 910 14 8 7 16 14 8 7 2 4 1 10 93 How? What are the differences and the similarities between these two heap trees?

6. Database Management Systems, R. Ramakrishnan and J. Gehrke 6 16 14 10 8 7 93 2 4 1 16 14 8 7 2 4 1 10 93

7. Database Management Systems, R. Ramakrishnan and J. Gehrke 7 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 16 14 8 7 2 4 1 10 93 14 8 4 7 2 1 10 93 16

8. Database Management Systems, R. Ramakrishnan and J. Gehrke 8 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 10 8 4 7 2 9 1 3 14 16 14 8 4 7 2 1 10 93 16

9. Database Management Systems, R. Ramakrishnan and J. Gehrke 9 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 9 8 4 7 3 12 10 14 16 10 8 4 7 2 9 1 3 14 16

10. Database Management Systems, R. Ramakrishnan and J. Gehrke 10 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 8 7 4 2 3 1 9 10 14 16 9 8 4 7 3 12 10 14 16

11. Database Management Systems, R. Ramakrishnan and J. Gehrke 11 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 7 4 1 2 3 8 9 10 14 16 8 7 4 2 3 1 9 10 14 16

12. Database Management Systems, R. Ramakrishnan and J. Gehrke 12 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 4 2 1 3 7 8 9 10 14 16 7 4 1 2 3 8 9 10 14 16

13. Database Management Systems, R. Ramakrishnan and J. Gehrke 13 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 3 2 1 4 7 8 9 10 14 16 4 2 1 3 7 8 9 10 14 16

14. Database Management Systems, R. Ramakrishnan and J. Gehrke 14 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 2 1 3 4 7 8 9 10 14 16 3 2 1 4 7 8 9 10 14 16

15. Database Management Systems, R. Ramakrishnan and J. Gehrke 15 In Memory Sorting: Heap-Sorting v Heap-Sort Procedure 4 1 3 2 16 9 10 14 8 7 Original Data Page 16 14 10 9 8 7 4 3 2 1 Sorted Data Page

16. Database Management Systems, R. Ramakrishnan and J. Gehrke 16 If file size is bigger than main memory, how can we do sorting? Data Storage Disk Main Memory I/O a. Partition file into small sub-files. b. Sorting these sub-files sequentially. I/O cost: # pass *pages*2

17. Database Management Systems, R. Ramakrishnan and J. Gehrke 17 2-Way Sort: Requires 3 Buffers v Pass 1: Read a page, sort it, write it. – only one buffer page is used v Pass 2, 3, …, etc.: – three buffer pages used. Main memory buffers INPUT 1 INPUT 2 OUTPUT Disk ---scan over the data set Only three pages of main memory are available! I/O cost: # pass *pages*2

18. Database Management Systems, R. Ramakrishnan and J. Gehrke 18 Two-Way External Merge Sort v Each pass we read + write each page in file. v N pages in the file => the number of passes v So total cost is: v Idea: Divide and conquer: sort subfiles and merge Input file 1-page runs 2-page runs 4-page runs 8-page runs PASS 0 PASS 1 PASS 2 PASS 3 9 3,4 6,2 9,48,75,63,1 2 3,45,62,64,97,8 1,32 2,3 4,6 4,7 8,9 1,3 5,62 2,3 4,4 6,7 8,9 1,2 3,5 6 1,2 2,3 3,4 4,5 6,6 7,8 16 I/O: 64

19. Database Management Systems, R. Ramakrishnan and J. Gehrke 19 General External Merge Sort v To sort a file with N pages using B buffer pages: – Pass 0: use B buffer pages. Produce sorted runs of B pages each. – Pass 2, …, etc.: merge B-1 runs. B Main memory buffers INPUT 1 INPUT B-1 OUTPUT Disk INPUT 2... * More than 3 buffer pages. How can we utilize them? ----each unit has B pages vs. 2 pages ---one page for output

20. Database Management Systems, R. Ramakrishnan and J. Gehrke 20 Cost of External Merge Sort v Number of passes: v Cost = 2N * (# of passes) v E.g., with 5 buffer pages, to sort 108 page file: – Pass 0: = 22 sorted runs of 5 pages each (last run is only 3 pages) – Pass 1: = 6 sorted runs of 20 pages each (last run is only 8 pages) – Pass 2: [6/4]=2 sorted runs, 80 pages and 28 pages – Pass 3: Sorted file of 108 pages ---use one page for output

21. Database Management Systems, R. Ramakrishnan and J. Gehrke 21 Number of Passes of External Sort

22. Database Management Systems, R. Ramakrishnan and J. Gehrke 22 I/O for External Merge Sort v … longer runs often means fewer passes! v Actually, do I/O a page at a time v In fact, read a block of pages sequentially! v Suggests we should make each buffer (input/output) be a block of pages. – But this will reduce fan-out during merge passes! – In practice, most files still sorted in 2-3 passes.

23. Database Management Systems, R. Ramakrishnan and J. Gehrke 23 Number of Passes of Optimized Sort * Block size = 32, initial pass produces runs of size 2B.

24. Database Management Systems, R. Ramakrishnan and J. Gehrke 24 Double Buffering v To reduce wait time for I/O request to complete, can prefetch into `shadow block’. – Potentially, more passes; in practice, most files still sorted in 2-3 passes. OUTPUT OUTPUT' Disk INPUT 1 INPUT k INPUT 2 INPUT 1' INPUT 2' INPUT k' block size b B main memory buffers, k-way merge

25. Database Management Systems, R. Ramakrishnan and J. Gehrke 25 Using B+ Trees for Sorting v Scenario: Table to be sorted has B+ tree index on sorting column(s). v Idea: Can retrieve records in order by traversing leaf pages. v Is this a good idea? v Cases to consider: – B+ tree is clustered Good idea! – B+ tree is not clustered Could be a very bad idea!

26. Database Management Systems, R. Ramakrishnan and J. Gehrke 26 Clustered B+ Tree Used for Sorting v Cost: root to the left- most leaf, then retrieve all leaf pages (Alternative 1) v If Alternative 2 is used? Additional cost of retrieving data records: each page fetched just once. * Always better than external sorting! (Directs search) Data Records Index Data Entries ("Sequence set")

27. Database Management Systems, R. Ramakrishnan and J. Gehrke 27 Unclustered B+ Tree Used for Sorting v Alternative (2) for data entries; each data entry contains rid of a data record. In general, one I/O per data record! (Directs search) Data Records Index Data Entries ("Sequence set")

28. Database Management Systems, R. Ramakrishnan and J. Gehrke 28 Summary v External sorting is important; DBMS may dedicate part of buffer pool for sorting! v External merge sort minimizes disk I/O cost: – Pass 0: Produces sorted runs of size B (# buffer pages). Later passes: merge runs. – # of runs merged at a time depends on B, and block size. – Larger block size means less I/O cost per page. – Larger block size means smaller # runs merged. – In practice, # of runs rarely more than 2 or 3.

29. Database Management Systems, R. Ramakrishnan and J. Gehrke 29 Summary, cont. v Choice of internal sort algorithm may matter: – Quicksort: Quick! – Heap/tournament sort: slower (2x), longer runs v The best sorts are wildly fast: – Despite 40+ years of research, we’re still improving! v Clustered B+ tree is good for sorting; unclustered tree is usually very bad.