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Witold Litwin Witold.Litwin@dauphine.fr Riad Mokadem Riad.Mokadem @dauphine.fr

Disk Backup Through Algebraic Signatures For A Scalable Distributed Data Structure in SDDS-2002 System. Witold Litwin Witold.Litwin@dauphine.fr Riad Mokadem Riad.Mokadem @dauphine.fr Thomas Schwartz tjschwarz@scu.edu. Plan. Introduction The SDDS-2002 Backup Scheme

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Witold Litwin Witold.Litwin@dauphine.fr Riad Mokadem Riad.Mokadem @dauphine.fr

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  1. Disk Backup Through Algebraic Signatures ForA Scalable Distributed Data Structurein SDDS-2002 System Witold Litwin Witold.Litwin@dauphine.fr Riad Mokadem Riad.Mokadem@dauphine.fr Thomas Schwartz tjschwarz@scu.edu

  2. Plan Introduction The SDDS-2002 Backup Scheme Experimental performance analysis. Conclusion.

  3. Introduction • Need for RAM SDDS storage to the disk • File Backup • Failure of a server • File Eviction • Sharing of RAM • Among different SDDS files • With other apps

  4. Introduction • Write to the disk only the parts (pages) changed since last backup • “Dirty bit” approach inapplicable • Page signature calculus: a possibility provided that: • Fast • Precise • Scalable • Shorter signatures may become longer without total recalculus • Not the case of SHA-1 nor of any other previous proposed schema

  5. Store command Multicast) … … … … Server RAM Buckets Distributed Storing The SDDS-2002 Backup SchemeFile Backup Client Server Disks        

  6. Distributed Loding The SDDS-2002 Backup SchemeFile Load Load command Multicast) Client … … … Server RAM Buckets         Server Disks

  7. Internal Organization of Bucket in SDDS Data File Index : a few Kbytes up to MByte Data file : Dozens of Mbytes up to GBytes

  8. Page Granularity • Carefull choice • Smaller page • More individual writes if many random updates • Less data transferred if a few updades • Larger pages • Vice versa • Optimal size ? • Good question • Our choice • 16 KB for data • Although64 KB pages proved best for data page signature calculus speed • 256 B for index

  9. Page Signature • Algebraic Signatures • Galois Field GF (216) • Log / Antilog multiplication • Page P has 2-byte symbols p1 , p2, ….pn • The signature formula is : • for each p’i = antilogp’i • for each  = : , 2, 3… • Sign ( P )= p’iii = 1..n • Sign (P)= (Sign ( P ), Sign 2( P ),…Sign m( P )) • We put m = 2 to SDDS-2002 i=1,2...n

  10. Experimental Performance AnalysisHardware Configuration • 1.8 GHz P4 Servers • 800 MHz P3 Client • 500 MHz P3 Name Server • 1 Gbs Ethernet • Windows 2000 Server OS

  11. Experimental Performance SDDS-2002Initial File Store Time (No Signature Calculus) Time (Sec) 120 100 80 60 40 20 File Size: 393MO 25 000 Records 1 2 3 4 File servers

  12. Initial File Store Time(Time Series) Storage Time (Ms) Number of record

  13. FileLoad Time (Sec) 120 100 80 60 40 20 File Size : 393MO 1 2 3 4 # of servers Practically the same as the 1st backup time

  14. Bucket size (MB) Number of record Signature calculus (ms) Signature Calculus per/MB (ms) Total store time (ms) Store time for 0 % change (ms) Gain (%) Store time for 5 % change (ms) Gain (%) 1.88 100 46 24.46 562 50 91.1 65 88.43 2.7 150 78 28.8 781 82 89.51 95 87.83 17.6 1000 438 24.88 5078 438 91.38 453 91.07 158 10000 4068 25.74 46406 4071 91.23 4085 91.19 393 25000 11003 27.9 117859 11003 91.33 11018 90.65 File Storage Performance Analysis

  15. Bucket size (Mb) Number of record Algebraic signature calculus (ms) SHA-1 calculus (ms) Initial Store time with SHA-1 (ms) Initial Store time with alg. sign. (ms) SHA-1 Store time for 5 % change (ms) Alg. sign Store time for 5 % change (ms) Gain (%) 1.88 100 46 70 602 562 85 65 30 2.7 150 78 103 799 781 119 95 25 17.6 1000 438 680 5278 5078 697 453 53 158 10000 4068 6088 47906 46406 6102 4085 49 393 25000 11003 15403 119342 117859 15418 11018 40 SHA-1 / Algebraic Signatures

  16. Algebraic / SHA-1 Signature Calculus Time

  17. Implementation in SDDS 2002Interactive Client Interface User interface

  18. Implementation in SDDS 2002Execution Listing at the Server 1st Request for storage : New File Signature Calculus (375 ms) Disk write of all pages (4922 ms) 2nd Request for storage : No changes found (375 ms) } 3rd Request for storage : 1 page changed (375 + 16 ms)

  19. Conclusion • The algebraic signature based file backup works • Present in SDDS-2002 prototype • Offers advantages over the traditional approach • No change to existing code • No run-time overhead • Future work • Signatures • Calculus, Alg. Properties, Apps… • Automatic SDDS File eviction

  20. Thank You forYour Attention

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