1 / 32

External Sorting

External Sorting. Chapter 13. Why Sort?. A classic problem in computer science! Data requested in sorted order e.g., find students in increasing gpa order Sorting is first step in bulk loading B+ tree index.

minya
Download Presentation

External Sorting

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. External Sorting Chapter 13

  2. Why Sort? • A classic problem in computer science! • Data requested in sorted order • e.g., find students in increasing gpa order • Sorting is first step in bulk loadingB+ tree index. • Sorting useful for eliminating duplicate copies in a collection of records • Sort-merge join algorithm involves sorting. • Problem: sort 1Gb of data with 1Mb of RAM. • why not virtual memory?

  3. Using secondary storage effectively • General Wisdom : • I/O costs dominate • Design algorithms to reduce I/O

  4. 2-Way Sort: Requires 3 Buffers • Phase 1: PREPARE. • Read a page, sort it, write it. • only one buffer page is used • Phase 2, 3, …, etc.: MERGE: • three buffer pages used. INPUT 1 OUTPUT INPUT 2 Main memory buffers Disk Disk

  5. Two-Way External Merge Sort 6,2 2 Input file 3,4 9,4 8,7 5,6 3,1 PASS 0 1,3 2 1-page runs 3,4 2,6 4,9 7,8 5,6 PASS 1 • Idea:Divide and conquer: sort subfiles and merge into larger sorts 4,7 1,3 2,3 2-page runs 8,9 5,6 2 4,6 PASS 2 2,3 4,4 1,2 4-page runs 6,7 3,5 6 8,9 PASS 3 1,2 2,3 3,4 8-page runs 4,5 6,6 7,8 9

  6. Two-Way External Merge Sort 6,2 2 Input file 3,4 9,4 8,7 5,6 3,1 PASS 0 1,3 2 1-page runs 3,4 2,6 4,9 7,8 5,6 PASS 1 • Costs for pass : all pages • # of passes : height of tree • Total cost : product of above 4,7 1,3 2,3 2-page runs 8,9 5,6 2 4,6 PASS 2 2,3 4,4 1,2 4-page runs 6,7 3,5 6 8,9 PASS 3 1,2 2,3 3,4 8-page runs 4,5 6,6 7,8 9

  7. Two-Way External Merge Sort 6,2 2 Input file 3,4 9,4 8,7 5,6 3,1 PASS 0 1,3 2 1-page runs 3,4 2,6 4,9 7,8 5,6 • Each pass we read + write each page in file. • N pages in file => 2N • Number of passes • So total cost is: PASS 1 4,7 1,3 2,3 2-page runs 8,9 5,6 2 4,6 PASS 2 2,3 4,4 1,2 4-page runs 6,7 3,5 6 8,9 PASS 3 1,2 2,3 3,4 8-page runs 4,5 6,6 7,8 9

  8. External Merge Sort • What if we had more buffer pages? • How do we utilize them wisely ? - Two main ideas !

  9. Phase 1 : Prepare INPUT 1 . . . INPUT 2 . . . INPUT B Disk Disk B Main memory buffers • Construct as large as possible starter lists.

  10. Phase 2 : Merge INPUT 1 Compose as many sorted sublists into one long sorted list. . . . INPUT 2 . . . OUTPUT INPUT B-1 Disk Disk B Main memory buffers

  11. General External Merge Sort • How can we utilize more than 3 buffer pages? • 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 1, 2, …, etc.: merge B-1 runs. INPUT 1 . . . . . . INPUT 2 . . . OUTPUT INPUT B-1 Disk Disk B Main memory buffers

  12. Cost of External Merge Sort • Number of passes: • Cost = 2N * (# of passes)

  13. Example • Buffer : with 5 buffer pages • File to sort : 108 pages • Pass 0: • Size of each run? • Number of runs? • Pass 1: • Size of each run? • Number of runs? • Pass 2: ???

  14. Example • Buffer : with 5 buffer pages • File to sort : 108 pages • 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: 2 sorted runs, 80 pages and 28 pages • Pass 3: Sorted file of 108 pages • Total I/O costs: ?

  15. Example • Buffer : with 5 buffer pages • File to sort : 108 pages • 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: 2 sorted runs, 80 pages and 28 pages • Pass 3: Sorted file of 108 pages • Total I/O costs: 2*N * (4 passes)

  16. Number of Passes of External Sort • gain of utilizing all available buffers • importance of a high fan-in during merging

  17. Optimizing External Sorting • Cost metric ? • I/O only (till now) • CPU is nontrivial, worth reducing

  18. Internal Algorithm : Heap Sort • Quicksort is a fast way to sort in memory. • An alternative is “tournament sort” (a.k.a. “heapsort”) • Top:Read in B blocks • Output:move smallest record to output buffer • Read in a new record r • insert r into “heap” • if r not smallest, then GOTO Output • else remove r from “heap” • output “heap” in order; GOTO Top

  19. Internal Sort Algorithm 2 8 10 12 3 . . . 4 5 INPUT CURRENT SET OUTPUT • 1 input, 1 output, B-2 current set • Main idea: repeatedly pick tuple in current set with smallest k value that is still greater than largest k value in output buffer and append it to output buffer

  20. Internal Sort Algorithm 2 8 10 12 3 . . . 4 5 INPUT CURRENT SET OUTPUT • Input & Output? new input page is read in if it is consumed, output is written out when it is full • When terminate current run? When all tuples in current set are smaller than largest tuple in output buffer.

  21. B More on Heapsort • Fact: average length of a run in heapsort is 2B • The “snowplow” analogy • Worst-Case: • What is min length of a run? • How does this arise? • Best-Case: • What is max length of a run? • How does this arise? • Quicksort is faster, but ...

  22. Optimizing External Sorting • Further optimization for external sorting. • Blocked I/O • Double buffering

  23. I/O for External Merge Sort • Thus far : do 1 I/O a page at a time • But cost also includes real page read/write time. • Reading a blockof pages sequentially is cheaper! • Suggests we should make each buffer (input/output) be a blockof pages. • But this will reduce fan-out during merge passes! • In practice, most files still sorted in 2-3 passes.

  24. I/O for External Merge sort • Example buffer blocks = b pagesset one buffer block for input, one buffer block for outputmerge |B-b/b| runs in each pass e.g., 10 buffer pages 9 runs at a time with one-page input and output buffer blocks 4 runs at a time with two-page input and output buffer block

  25. Double Buffering – Overlap CPU and I/O • 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. INPUT 1 INPUT 1' INPUT 2 OUTPUT INPUT 2' OUTPUT' b block size Disk INPUT k Disk INPUT k' B main memory buffers, k-way merge

  26. Sorting Records! • Sorting has become a blood sport! • Parallel sorting is the name of the game ... • Datamation: Sort 1M records of size 100 bytes • Typical DBMS: 15 minutes • World record: 3.5 seconds • 12-CPU SGI machine, 96 disks, 2GB of RAM • New benchmarks proposed: • Minute Sort: How many can you sort in 1 minute? • Dollar Sort: How many can you sort for $1.00?

  27. Using B+ Trees for Sorting • Scenario: Table to be sorted has B+ tree index on sorting column(s). • Idea: Can retrieve records in order by traversing leaf pages. • Is this a good idea? • Cases to consider: • B+ tree is clusteredGood idea! • B+ tree is not clusteredCould be a very bad idea!

  28. Clustered B+ Tree Used for Sorting • Cost: root to left-most leaf, then retrieve all leaf pages (Alternative 1) • For Alternative 2, additional cost of retrieving data records: each page fetched just once. Index (Directs search) Data Entries ("Sequence set") Data Records • Always better than external sorting!

  29. Unclustered B+ Tree Used for Sorting • Alternative (2) for data entries; each data entry contains rid of a data record. • In general, one I/O per data record! Index (Directs search) Data Entries ("Sequence set") Data Records

  30. External Sorting vs. Unclustered Index • p: # of records per page • B=1,000 and block size=32 for sorting • p=100 is the more realistic value.

  31. Summary • External sorting is important; DBMS may dedicate part of buffer pool for sorting! • External merge sort minimizes disk I/O costs: • 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.

  32. Summary, cont. • Choice of internal sort algorithm may matter. • The best sorts are wildly fast: • Despite 40+ years of research, we’re still improving! • Clustered B+ tree is good for sorting; unclustered tree is usually very bad.

More Related