d a ee a aes e ed

1
????d?? ?a? ?e???????e? ??a ??a?e???s? ?e?????
????? ?ed?µ????
??d?s???te? ?a???? ???st?? e-mail
makri_at_ceid.upatras.gr ??das?a??a ??µpt?
1700-1900 ?200
2
?e????af? t?? ?a??µat??

• ?? µ???µa ape????eta? se ?s??? f??t?t?? ?????? ?a
  ap??t?s??? ßas???? ???se?? st?? pe????? t?? d?µ??
  ded?µ???? ?a? t?? a??????µ???? te?????? p??
  s?et????ta? µe t? d?a?e???s? ?a? epe?e??as?a
  µe????? ????? ded?µ????.  
• S?et???µe?a ?a??µata ??µ?? ?ed?µ????,
  ???????µ??e? ??µ?? ?ed?µ???? ?a? G?af???, Te???a
  ?as???? ??µ?? ?ed?µ????, ???????µ??,  ?e???????e?
  ???p???s?? ???????µ??. ??f?a?? ?pe?e??as?a ?a?
  ?????s? ?????a?, ????t?s? ?????f???a?, ??se??
  ?ed?µ???? I,II. 

3
??t??e?µe?a p?? ?a??pt??ta?

• ?a ??µata p?? ?a??pt??ta? st? µ???µa e??a? ta
  a??????a
• 1.        ???t??a ?e?te?e???sa? ???µ?? (???t???
  d?? ep?p?d??, ?e?a????? µ??t??a, Cache Oblivious
  µ??t??a).
• 2.        ???????µ?? ?a? ??µ?? ?ed?µ???? ??a
  µ??t??a d?? ep?p?d??  (B-Trees, Weight Balanced
  B-Trees, Buffer Trees)
• ???????µ?? ?p?????st???? Ge?µet??a? st?
  ?e?te?e???sa ???µ?.
• ???????µ?? ??a p??ß??µata ???es?? ?e?????? st?
  ?e?te?e???sa ???µ?.
• ???????µ?? ??a?e???s?? S?µß???se???? st?
  ?e?te?e???sa ???µ?
• 6.        ???????µ?? ?a? ??µ??  ?ed?µ???? ??a
  Cache Oblivious ???t??a (Cache Oblivious B-Tree,
  Cache Oblivious ????? ???te?a??t?ta?, Ge?µet?????
  ???????µ?? st? Cache Oblivious ???t???
  ?p?????sµ??) .
• 7.        A??????µ?? st? ???t??? ???? ?ed?µ????.
• 8.         ?fa?µ????  (X??????? ??se?? ?ed?µ????,
  ???????????? ??se?? ?ed?µ????, ????µes???? ??se??
  ?ed?µ????).

4
??ad??ast???

• ???tas? (p??f?????)
• ???as?a
• ?a???s?as?
• G?apt? ??af???
• ?e????? ?a?µ??
• ?µ??????sµa

5
??sta ???as???

• External Memory Data Structures
• Vitter, J. S. and Shriver, E. 1994a. Algorithms
  for parallel memory I Two-level memories.
  Algorithmica 12, 23, 110147.
• Vitter, J. S. and Shriver, E. A.1994b. Algorithms
  for parallel memory II Hierarchical multilevel
• S. Lanka, E. Mays, Fully Persistent B-trees, ACM
  International Conference on Management of Data,
  426-435, 1992.
• Varman P. Verma R. An Efficient Multiversion
  Access Structure. IEEE Transactions on Knowledge
  and Data Engineering, 391-409. 1997
• B. Becker, S. Gschwind, T. Ohler, B. Seeger, P.
  Widmayer, An asymptotically optimal multiversion
  B-tree, The VLDB Journal, 264-275.
• P. Ferragina and R. Grossi. The string B-tree a
  new data structure for string search in external
  memory and its applications. J. ACM,
  46(2)236-280, 1999.

6

• External Memory Geometric Data Structures
• Arge, L. 1995a. The buffer tree A new technique
  for optimal I/O-algorithms. In Proceedings of the
  Workshop on Algorithms and Data Structures, Vol.
  955 of Lecture Notes in Computer Science,
  Springer-Verlag, 334345, 1995. A complete
  version appears as BRICS Technical Report
  RS9628, University of Aarhus.
• Arge, L. 1997. External-memory algorithms with
  applications in geographic information systems.
  In M. van Kreveld, J. Nievergelt, T. Roos, and
  P. Widmayer, eds, Algorithmic Foundations of GIS,
  Vol. 1340 of Lecture Notes in Computer Science,
  Springer-Verlag, 213254.
• Arge, L. and Vahrenhold, J. I/O-efficient
  dynamic planar point location. In Proceedings of
  the ACM Symposium on Computational Geometry
  (June), Vol. 9, 191200, 2000.
• Kanellakis, P. C.,Ramaswamy, S., Vengroff, D.
  E., and Vitter, J. S. 1996. Indexing for data
  models with constraints and classes. Journal of
  Computer and System Sciences 52, 3, 589612.
• Arge, L. and Vitter, J. S. Optimal dynamic
  interval management in external memory. In
  Proceedings of the IEEE Symposium on Foundations
  of Computer Science, 1996.
• Arge, L., Samoladas, V., and Vitter, J. S. 1999b
  Two-dimensional indexability and optimal range
  search indexing. In Proceedings of the
  ACMConference Principles of Database Systems
  (Philadelphia, MayJune), Vol. 18, 346357, 1999.

7

• Cache Oblivious Data Structures
• M. Frigo, C.E. Leiserson, H. Prokop, and S.
  Ramachandran. Cache-oblivious algorithms. In
  Proc. 40th IEEE Symp. on Foundations of Computer
  Science (FOCS 99), pages 285-297, 1999.
•  M. A. Bender, E. Demaine, and M.
  Farach-Colton.Cache Oblivious B-Trees"
  Proceedings of the 41st Annual Symposium on
  Foundations of Computer Science (FOCS), pages
  399-409, 2000.
• Gerth St?lting Brodal and Rolf Fagerberg, Funnel
  Heap A Cache Oblivious Priority Queue,  In
  Proc. 13th Annual International Symposium on
  Algorithms and Computation, volume 2518 of
  Lecture Notes in Computer Science, pages 219-228.
  Springer Verlag, Berlin, 2002 
• Gianni Franceschini, Roberto Grossi, J. Ian
  Munro, and Linda Pagli. Implicit B-trees A New
  Data Structure for the Dictionary Problem.
  Journal of Computer and System Sciences, special
  issue of the 43th Annual IEEE Symposium on
  Foundations of Computer Science (FOCS), 2004.  
• Gianni Franceschini and Roberto Grossi. Implicit
  dictionaries supporting searches and amortized
  updates in O(log n loglog n). In Proceedings of
  the 14th Annual ACM-SIAM Symposium on Discrete
  Algorithms (SODA), pages 670-678. SIAM, 2003.
• Gianni Franceschini and Roberto Grossi. Implicit
  dictionaries supporting searches and amortized
  updates in O(log n loglog n). In Proceedings of
  the 14th Annual ACM-SIAM Symposium on Discrete
  Algorithms (SODA), pages 670-678. SIAM, 2003.

8

• External Memory Algorithms
• A. Broder and M. Henzinger. Algorithmic Aspects
  of Information Retrieval on the Web, Handbook of
  Massice Data Sets, ed. Abello, Pardalos, Resende.
  
• M.Najork, A. Heydon, High Performance Web
  Crawling, Handbook of Massice Data Sets, ed.
  Abello, Pardalos, Resende.
• W. Aiello, F. Chung, L. Lu, Random Evolution in
  Massive Graphs. Handbook of Massice Data Sets,
  ed. Abello, Pardalos, Resende.
• O. Goldreich, Property Testing in Massive Graphs,
  Handbook of Massice Data Sets, ed. Abello,
  Pardalos, Resende.
• R. Baeza-Yates, A. Moffat, G. Navarro, Searching
  Large Text Collections, Handbook of Massice Data
  Sets, ed. Abello, Pardalos, Resende.
• J. Dula, F. Lopez, Data Envelopment Analysis
  (DEA) in Massive Data Sets, Handbook of Massice
  Data Sets, ed. Abello, Pardalos, Resende.
• P. Bradley, O. Mangasarian, D. Musicant,
  Optimization Methods in Massive Data Sets, in
  Massive Data Sets, Handbook of Massice Data Sets,
  ed. Abello, Pardalos, Resende.
• F. Murtagh, Clustering in Massive Data Sets, in
  Massive Data Sets, Handbook of Massice Data Sets,
  ed. Abello, Pardalos, Resende.
• M. Riedewald, D. Agrawal, A. Abbadi, Managing and
  Analyzing Massive Data Sets with Data Cubes, in
  Massive Data Sets, Handbook of Massice Data Sets,
  ed. Abello, Pardalos, Resende.
• M. Goodchild, K. Clarke, Data Quality in Massive
  Data Sets in Massive Data Sets, Handbook of
  Massice Data Sets, ed. Abello, Pardalos, Resende.
  
• T. Johnson, Data Warehousing, Handbook of Massice
  Data Sets, ed. Abello, Pardalos, Resende.
• Q. Ma, M. Wang, J. Gatliker, Mining Biomolecular
  Data Using Background Knowledge and Artificial
  Neural Networks, Handbook of Massice Data Sets,
  ed. Abello, Pardalos, Resende.

9
RAM ???t??? ?p?????sµ??

• ?as??? ?e???t??? µ??t??? ?p?????sµ??
• ?pe??? µ??µ?
• ?µ???µ??f? ??st?? p??sp??as??
• ?p?? µ??t??? p??????st? se efa?µ???? t??
  p????f??????

10
?e?a???a ???µ?? ??p???? ???a??µat??
11
??a?t??? T?µata

• Caching
• Virtual Memory
• Secondary Storage
• - Disk Floppy (hard, soft)
• Winchester
• Ram Disks
• Optical, CD-Rom
• Arrays
• Tape Reel, Cartirdge
• Robots

12
Xa?a?t???st??? ?a???t???? ??s???

• ? p??sp??as? st? d?s?? e??a? 106 f???? p?? a???
  ap? t? p??sp??as? t?? ????a? µ??µ??

• ?a s?st?µata d?s??? ep??e????? ?a ep?µe??s???
  µe?????? ??????? p??sp??as?? µetaf????ta? µe???a
  s??e?? blocks ded?µ???? (8-16Kbytes)
• S?µa?t??? ? ap????e?s?/p??sp??as? ded?µ???? ?a
  e?µeta??e?eta? t?? pa?e??µe?e? d??at?t?te?
  ?µad?p???s??.

13
??p???? ???????? ????p????t?te?

• Seek Time (?????? e?t?p?sµ??)
• 10 -40 ms
• Rotational Delay (?????? ?a??st???s??
  pe??st??f??)
• 4.16 ms
• Block Transfer Time (?????? µetaf???? block)
• t 10 - 50 MB/sec
• block size 32Kb, t32MB/second, pa???e? ?????
  µetaf???? block 1 ms
• ??af??? Random ap? Sequential I/O
• ??st?? ????af?? pa??µ??? µe ??????s??

14
???ß??µata ?etafe?s?µ?t?ta?

• ????? p?????µµata p?? ????? a?apt???e? ??a t?
  RAM µ??t???
• t?????? se µe???a s????a ded?µ???? ??at? t? ?/S
  µeta???e? ta blocks ?? ?fe??e?
• ?a µ??t???a ?/S ???s?µ?p????? p???p???e? paging
  ?a? prefetching st?at??????
• e?t??t??? a? t? p????aµµa p?a?µat?p??e?
  d?as???p?sµ??e? p??spe??se?? a??µa ?a? ta ?a??
  ?/S de? µp????? ?a a???p???s??? t?? block
  p??spe??se??.

15
???t??a ?e?a?????? ???µ??
16
??ep?pede? ?e?a???e? ???µ??

• ?ed?µ??a p??ß??µ?t?? st? d?s??
• ???d?? p??ß??µ?t?? st? d?s??
• ???????µ??? ??st?? e??a? ?? p???e??
  e?s?d??/e??d??
• ?a st???e?a ?µad?p?????ta? se blocks µe?????? B

17
?a??????a ?p?s?st?µata ??s???

• ?? pe?????sµ??? pa??????? µ??t??? (?ggarwal and
  Vitter 1987)
• ?p???e? p???? ep?peda d?s???
• ?a a?t??e?µe?a ?µad?p?????ta? st? d?s??, µe B
  a?t??e?µe?a a?? block
• ?p???d?p?te ap? D blocks µp??e? ?a ??afe? ?a? ?a
  d?aßaste? ta?t?????a se ??a I/O

• ?a??????? µ??t??? d?s??? (?ggarwal and Vitter
  1987)
• ?p???e? µ?a µ???da epe?e??as?a?, µ?a µ???da
  µ??µ?? ?a? D µ???de? d?s???
• D blocks µp????? ?a d?aßast???/??af???
  ta?t?????a, a??? µ??? e?? ß??s???ta? se
  d?a???t??? d?s????
• ??? ?ea??st??? µ??t??? ap? t? µ? pe?????sµ???
  pa??????? µ??t???
• H CPU µp??e? ?a e??a? t? s?µe?? ad?e??d?? e?? t?
  D e??a? a??et? µe????.

• ?a??????e? ?e?a???e? ???µ?? (?ggarwal and Vitter
  1987)
• H ?e?a???e? t?? ?d??? t?p?? (µe H CPUs)
  s??d???ta? µe ??a d??t??
• ? a???µ?? t?? d?s??? D µp??e? ?a e??a?
  pe??ss?te???, ?d??? ? µ????te??? ap? t?? a???µ?
  t?? epe?e??ast??

18
????ep?pede? ?e?a???e? ???µ??

• Hierarchical Memory Model (Aggarwal, Alpern,
  Chandra, Snir 1987)
• ?p?????? p???? ep?peda d?s???
• ???sp??as? st? ??s? µ??µ?? x apa?te? ????? f(x)
• ? f e??a? µ?a a????sa s????t?s? ?ts? ?ste ?a
  ?p???e? sta?e?? c ?p?? f(2x) cf(x) ??a ???e x

• Block Transfer Model (Aggarwal, Chandra, Snir
  1987 )
• ?p?????? p???? ep?peda d?s???
• ???sp??as? st? ??s? µ??µ?? x apa?te? ????? f(x)
• .?p? t? st??µ? p?? ??e? p?a?µat?p????e?
  p??sp??as?, ep?p???? a?t??e?µe?a µp????? ?a
  e?te???? st? ??st?? t?? e??? a?? a?t??e?µe???.

• Uniform Memory Hierarchies (Alpern, Carter, Feig
  1990)
• ?p???e? ?e?a???a µ??µ?? e??et???? µe??????
• ???e d?a???? s?et??eta? µe ??a bandwidth
• ???? ?? d?a???? µp??e? ?a e??a? e?e????
  ta?t?????a

19
Cache Oblivious ???t??? (1)

• ?st? µ?a ?e?a???a µe t??a ep?peda (p.?. Cache,
  RAM, d?s??)
• ?st? ?t? ? µetaf??? block se ?aµ???te?a ep?peda
  ???eta? se B1 ???e?? ?a? sta ?????te?a se B2
  ???e??.
• ??? ?a µp????se ?a s?ed?aste? a??????µ?? p?? ?a
  pa???e? ?p???? t?? ?a? B1 ?a? ?2

20
Cache Oblivious ???t??? (2)

• ??a ep?ped? st?? ?e?a???a pa??e? t? ???? t??
  cache ??a t? ep?µe?? ep?ped?.
• ? d?ad??as?a caching e????eta? se hardware ?a?
  software.
• ?????? st?at?????? caching LRU, FIFO
• S?????? pe?????sµ??e? e?d???? t?? LRU, FIFO. ???
  s???e???µ??a st?? p???? ????µe pe?????sµ???
  associativity ? a???µ?? t?? p??a??? ??se?? ??a
  d???? block e??a? ??a? µ????? a???µ?? k.

21
Cache Oblivious ???t??? (3)

• ??? ep?p?d?? ?e?a???a
• Cache µe?????? M
• Cache-line µ????? B
• ?????? associative
• ???t?st? a?t??at?stas?

22
Cache Oblivious ???t??? (4)

• ?as???? ?p???se??
• ??? ep?p?d?? ?e?a???a
• Tall Cache Assumption MO(?2)
• ???t?st? p???t??? Cache Replacement
• Cache Oblivious ???????µ??
• ???????µ?? p?? de? ??e???eta? ?a ???e? M, B.
• St?? a????s? t?? a??????µ?? ?? p???p????t?te?
  e?f?????ta? ?? s??a?t?se?? t?? M ?a? ?
• ??aµ????µe pa??µ??a p???p????t?ta µe a?t? t??
  ??ass???? µ??t????.
• ?????? ???????µ??
• ??a? Cache-Oblivious a??????µ?? e??a? a?t?µata
  ß??t?st?? ??a ??a ta ep?peda µ?a? ?e?a???a?
  µ??µ??.

23
?as??? ???t???

• N st???e??? st? p??ß??µa
• B st???e??? st? disk block
• M st???e??? st? ????a µ??µ?
• T st???e??? st?? ???d?
• I/O ?eta????s? block µeta?? µ??µ?? ?a? d?s???
• ?p???t??µe ?t? M gtB2
• ???p?? µ?t??s?? t?? ap?d?s??
• ????µ?? ?/?s
• ????? t?? d?s??? p?? ???s?µ?p??e?ta?
• ?????? ?p?????sµ?? p?? apa?te?ta?
• ?? s?µa??e? ß??t?st? p???p????t?t?
• ??af???p???s? a??µesa se on-line ?a? off-line
  ?p?????sµ???.

24
?as???? ?e?????? (off-line)

• Merge-Sort like techniques
• Distribution Sorting techniques
• Distribution sweeping
• Persistent B-Trees (off-line te?????, ße?t???e?
  ?at? B t?? on-line te?????)
• Batched Filtering (te????? ta?t??????? ?a??µ?t??,
  se d?µ?? p?? µp????? ?a µ??te??p??????? sa
  d???af?µata)
• External Fractional Cascading
• External Marriage Before Conquest
• Batched Incremental Construction

25

• Off-line Computational Geometry
• 1. Computer intersection of N plane segments and
  their trapezoidal decomposition.
• 2. Find all intersections between N
  nonintersecting red line segments and N
  nonintersecting blue line segments in the plane.
• 3. Answer Q orthogonal 2-D range queries on N
  points in the plane.
• 4. Construct the 2-D and 3-D convex hull of N
  points.
• 5. Voronoi diagram and triangulation of N points
  in the plane.
• 6. Perform Q point location queries in a planar
  subdivision of size N.
• 7. Find all nearest neighbors for a set of N
  points in the plane.
• 8. Find the pairwise intersections of N
  orthogonal rectangles in the plane.
• 9. Compute the measure of the union of N
  orthogonal rectangles in the plane.
• 10. Compute the visibility of N segments in the
  plane from a viewpoint.
• 11. Perform Q ray-shooting queries in 2-D
  Constructive Solid Geometry (CSG)

26
(No Transcript)
27
?as???? ????p????t?te?

• Internal External
• Scanning N
• Sorting N log N
• Permuting
• Searching
• ?a?at???se??
• G?aµµ??? I/O O(N/B)
• ??ad??ta?? µ? ??aµµ???
• ?? ?????? a?ad??ta??? ?a? d??ta??? e??a? p?a?t???
  ?s??
• B pa?????ta? ???? s?µa?t????
• ?e? µp??e? ?a d?at??e? ß??t?sta

28
???ta??

• ltM/B d?ateta?µ??e? ??ste? (?????) µp????? ?a
  s?????e????? se O(N/B) I/Os
• 
  
• ?? d?ateta?µ??? ??sta µp??e? ?a d?a????ste?
  ???s?µ?p????ta? ltM/B st???e?a d??spas?? se
  O(N/B) I/Os

29
???ta??

• Merge sort
• ??µ??????se N/M memory sized d?ateta?µ??e? ??ste?
• ?pa?a?aµßa??µe?a s?????e?se ??ste? T(M/B) t? f???
  
• f?se?? µe
  I/Os ? ?a?eµ?a? ?/?s
  

30
???????? HASHING

• ??? ?at?????e?
• Directory
• Directoryless
• Directory
• ???a?a? µe?????? 2d ap? ?e???
• ?a a?t??e?µe?a ap????e???ta? se ?e??? a?????a µe
  ta d te?e?ta?a bits t?? hash d?e????s?? t???
• ???e ?e?? ??e? ??a de??t? p??? t? block p??
  ap????e???ta? ta a?t??e?µe?a
• 2 ?/?s a?? a?a??t?s?
• ???spas? ?a? s?????s? ?e????.
• ???e ?e?? ??e? ??a t?p??? ß???? b. ?p??e? ?a
  µ?????eta? t? ?d?? block µe ???a ?e???
• Blocks ?at? 67 ?eµ?ta

• Directoryless
• - ???s?µ?p?????ta? ??ste? ?pe??e???s?? ?a?
  ta blocks d?asp??ta? µe p???a????sµ??? se???.

31
SPATIAL ????S ???????O?

• ?p????e?s? ?a? e??t?s? ded?µ???? ?????
• ??? e?d? ??????? d?µ??
• Data-driven
• ?as????ta? st? d?a????sµ? t?? ?d??? t??
  a?t??e?µ????
• ?.? R-trees, kd-trees
• Space-driven
• ??a????sµ?? t?? ????? t?? a?t??e?µ????
• ?.? quad d??t?a, a??e?a grid
• ?ß??d???? d?µ??
• Cross tree
• D-d??stat? ??d?s? t?? ?-tree
• Data-driven d?a????sµ?? sta p??? ep?peda,
  space-driven ??t?
• ???t?se?? se
• ??sa????? d?a??af?? se

32
??ß?????af?a

• Aggarwal and Vitter, 1988. The input/output
  complexity of sorting and related problems.
  Communications of the ACM 31, 9, 1116-1127
• Aggarwal, Alpern, Chandra, Snir, A model for
  hierarchical memory. In Proceedings of the IEEE
  Symposium on Foundations of Computer Science, 19,
  305-314
• Aggarwal, Chandra, Snir, Hierarchical memory with
  block transfer. In Proceedings of the IEEE
  Symposium on Foundations of Computer Science, 28,
  204-216.
• Vitter and Shriver, Algorithms for parallel
  memory I Two-level memories. Algorithmica 12
  2-3, 10-147.
• Vitter and Shriver, Algorithms for parallel
  memory II Hierarchical multilevel memories.
  Algorithmica 12 2-3, 148-169.
• J. Abello, P. Pardalos, M. Resende, Handbook of
  Massive Data Sets

33
??apa??stas? ?ed?µ?????e?a?????? ??µ??
?e??t?d?t?s??
34
Block Addresses in Main and Secondary Memory
Block address for blocks in main memory The block
has a virtual memory address when it is loaded
into a buffer in main memory Block address for
blocks in secondary memory The block has no
virtual memory address. The physical address
space has to be used. The physical address
describes the physical location of the block.
35
Physical and logical addresses
Physical Address Describes physical location,
i.e. disk, cylinder, track numbers. Typical size
8-16 bytes. Logical address A fixed length
arbitrary string for each record. A table is
used to map logical addresses to physical
addresses.
36
B-Tree

• B-d??t?? µe ßa?µ? e??d?? b ?a? pa??µet?? f????? k
  (b,k8)
• ??a ta f???a e??a? st? ?d?? ep?ped? ?a? pe???????
  a??µesa ap? 1/4k ?a? k st???e?a
• ??t?? ap? t? ???a, ???? ?? ??µß?? ????? ßa?µ?
  e??d?? µeta?? 1/4b ?a? b
• ? ???a ??e? ßa?µ? e??d?? µeta?? 2 ?a? b
• B-d??t?? µe pa??µet?? f?????
• O(N/B) ?????
• ????
• ep?µe??sµ??? ??st??
  epa?a????s?? f?????
• amortized internal node
  rebalance operations
• B-tree with branching parameter Bc, 0ltc1, and
  leaf parameter B
• Space O(N/B), updates ?(logBNk/B), queries
• Variations B (leaf links), B (variations of
  B, with no splitting, sharing if possible).

37
???????? HASHING

• ??? ?at?????e?
• Directory
• Directoryless
• Directory
• ???a?a? µe?????? 2d ap? ?e???
• ?a a?t??e?µe?a ap????e???ta? se ?e??? a?????a µe
  ta d te?e?ta?a bits t?? hash d?e????s?? t???
• ???e ?e?? ??e? ??a de??t? p??? t? block p??
  ap????e???ta? ta a?t??e?µe?a
• 2 ?/?s a?? a?a??t?s?
• ???spas? ?a? s?????s? ?e????.
• ???e ?e?? ??e? ??a t?p??? ß???? b. ?p??e? ?a
  µ?????eta? t? ?d?? block µe ???a ?e???
• Blocks ?at? 67 ?eµ?ta

• Directoryless
• - ???s?µ?p?????ta? ??ste? ?pe??e???s?? ?a?
  ta blocks d?asp??ta? µe p???a????sµ??? se???.

38
SPATIAL ????S ???????O?

• ?p????e?s? ?a? e??t?s? ded?µ???? ?????
• ??? e?d? ??????? d?µ??
• Data-driven
• ?as????ta? st? d?a????sµ? t?? ?d??? t??
  a?t??e?µ????
• ?.? R-trees, kd-trees
• Space-driven
• ??a????sµ?? t?? ????? t?? a?t??e?µ????
• ?.? quad d??t?a, a??e?a grid
• ?ß??d???? d?µ??
• Cross tree
• D-d??stat? ??d?s? t?? ?-tree
• Data-driven d?a????sµ?? sta p??? ep?peda,
  space-driven ??t?
• ???t?se?? se
• ??sa????? d?a??af?? se

39
?e?te?e???se? ??µ??

• ?ta? ???s?µ?p?????ta? d?µ?? de?te?e???sa?
  ap????e?s??, µ?a epa?a????s? st? v ?a e??a? ?a??
  ?a ??st??e? O(w(v)) I/Os (w(v) e??a? t? ß???? t??
  v)
• ??? e???se?? p??pe? ?a pe??s???
  ap? t? v
• ? O(1) ep?µe??sµ??? ??st?? d??spas??
• ? ep?µe??sµ??? ??st?? ???es??
• ?? ??µß?? st? ??ass??? B-tree de? ????? t??
  ?d??t?ta a?t?

40
??a-Tree

• BB?-d??t?a ????? t?? ?d??t?ta a?t?
• ????eta? µe ?d??t?te? ß?????
• ?? p????? a??µesa st? ß???? t?? a??ste??? pa?d???
  ?a? t?? de???? pa?d??? e??a? µeta?? ? ?a? 1-?
• ?
• ???? O(log N)
• ??? epa?a????s?
  µp??e? ?a ???e? µe ???s? pe??st??f??
• Fa??eta? d?s???? ?a ???p??????? ta BB?-d??t?a
  I/O-ap?te?esµat???

41
Weight-balanced B-tree

• S??d?asµ?? B-tree ?a? BB?-tree
• ?e?????sµ?? ß????? a?t? ßa?µ??
• ?pa?a????s? µe d??spas?/s?????e?s? ?p?? se B-tree
• Weight-balanced B-tree µe pa?aµ?t???? b ?a? k
  (bgt8, k8)
• ??a ta f???a st? ?d?? ß???? ?a?
• pe??????? µeta?? k/4 ?a? k st???e?a
• ?s?te????? ??µß?? v st? ep?ped? l ??e?
• w(v) ltblk
• ??t?? ap? t? ???a, es?te????? ??µß?? v
• st? ep?ped? l ??e? w(v)gt(1/4) blk
• ? ???a ??e? p?? p???? ap? ??a pa?d??.

42

• ???e es?te????? ??µß?? ??e? ßa?µ? µeta?? b ?a?
  4b. ????-gtO(logBN/k)
• Extern
• Choose 4bB (or even Bc for 0 lt c 1)
• kB
• ?
• O(N/B) ?????,
  ?????? e??t?s??

43
Weight-balanced B-tree ???es?

• ???e ??a s?et??? f???? u ?a? ???ese ??? st???e??
• ??ap??ase µ???p?t? ap? f???? u se ???a
• ??? ? ??µß?? v ep?p?d?? l ??e? w(v)blk1 pa?d??
• sp?se t?? ??µß? se ??µß??? v ?a? v with
  
• 
  ?a?
• ???????µ?? s?st?? ef?s??
  
• ?ts? ?ste ?a?
• ???spe?a????ta? ??µß??
• ?d??t?ta ßa??????s??
• - O(blk) e??µe??se?? ??t? ap? v ?a? v p???
  ep?µe?? p????.

44
Weight-balanced B-tree ??a??af?

• ???e ??a s?et??? f???? u ?a? d????a?e st???e??
• ??ap??ase µ???p?t? ap? u st? ???a
• ??? ? ep?p?d?? l ??µß?? v ??e? t??a
• t?te s?????e?se µe sibling st? ??µß? v
• ?p??
• ??? then split into
  nodes
• µe ß????
• ?a?
• ???????µ?? s?st?? ?a? a???µp?
  ??µß???
• ?d??t?ta ß?????
• p???e?? ??t? ap? v ?a? v p???
  t?? ep?µe?? p????

45
S????? Weight-balanced B-tree

• ?a??????sµ??? B-tree µe ßa?µ? e??d?? b ?a?
  pa??µet?? f????? k?(B)
• O(N/B) ?????
• ????
• p???e?? epa?a????s?? µet?
  ap? e??µ???s?
• ?(w(v)) e??µe??se?? ??t? ap? t? v a??µesa ap?
  s??e??µe?e? p???e?? v
• ?a??????sµ??? B-tree µe ßa?µ? e??d?? Bc ?a?
  pa??µet?? f????? B
• ???µe??se?? ?a? e??t?se?? se
  I/Os
• ??µ?s? ap? ??t? p??? ta ??? se
  I/Os

46
??a???????t?ta
???????? ??se?? ?ed?µ????
??se?? ?ed?µ???? ?????? ??s?????a? (Transaction
Time) ??at????? t?? ?st???a t?? d?ast????t?t??
t???. ???e d?s?????a µe t? ??s? ?ed?µ????
p??sd?????eta? µe µ?a ??????? ??de???. ???a?
ef??t? ? p??sp??as? d?af??et???? ????????
st??µ??t?p?? t?? ??s?? ?ed?µ????. ??se??
?ed?µ???? ?s????t?? ?????? (Valid Time) ??at?????
a?t??e?µe?a p?? µ?a s???st?sa t??? ?p?d????e?
??????? st??µ??t?pa. ?? s????? t?? t?µ?? a?t??
ap????e???? t?? t?????? ???se?? ??a t? pa???, t?
pa?e???? ? a??µa ?a? t? µ????? t?? ap????e?µ????
a?t??e?µ????. ?????????? ??se?? ?ed?µ????
(Bitemporal) ?p?te???? s??d?asµ? t?? d?? pa?ap???
?at???????. ??apa??st??? t?? p?a?µat???t?ta
ep?t??p??ta? e?te a?ad??µ???? e?te e? t?? ?st????
a??a???.
47
??se?? ?ed?µ???? ?????? ??s?????a?
??????? ???????
48
??se?? ?ed?µ???? ?s????t?? ??????
??????? ???????
49
?????????? ??se?? ?ed?µ????
??????? ???????
50
??a???????t?ta-?????e?
??µ?? ?ed?µ????
G?aµµ??? a???????a e?d????
?f?µe?e?
??a????????
???? µ?a e?d???
?e?????
i
i1
i2
i
??????
i
?e?t???? d?µ? e?d????
i1
i4
i2
i
i3
i3
i4
i2
i5
S??e??t????
i6
DAG e?d????
51
?etat??p? ?f?µe??? ??µ?? se ?e????? ??a???????
(Driscoll et al. 89)
??? ?e????? µ???d?? ??a d?as??deµ??e? d?µ??
a) fat-node

• pepe?asµ??? s????? ??µß?? µe sta?e?? a???µ?
  ped??? (ded?µ??a ?a? de??te?)
• sta?e?? a???µ? ??µß?? e?s?d??

??????(1)/e??µe?.
???????(logm)/e??µe?.? p??sp??as?
ß) node-copying
?p?µe??sµ???? ??????(1)/e??µ???s?
?p?µe??sµ???? ??????(1)/e??µ???s?
52
Fat Node ????d??
?f?µe??? ??µß??
??d?s? ??µß??
??a???????? ??µß??
??µ? ?ed???
???µa ?ed???
??d?s?
53
Node-Copying ????d??
??µß?? pe?????sµ???? ????t???t?ta? ?ta? ? ??µß??
?eµ?se? d?µ???????µe ??? a?t???af? t?? ??µß??
e??µ???s? ped???
?pe?d? p??pe? ?a e??a? ef??t? ? p??sp??as? e???
???? ??µß?? p??pe? ?a a?t???????µe t??? ?µes???
p???????? t?? ? ? µ???d?? d??e? ??a sta?e??
ep?µe??sµ??? ??st?? ?ta? ? ßa?µ?? e?s?d?? ???e
??µß?? e??a? f?a?µ????.
54
??a??????? ?-Tree

• ?e???? ??a???????t?ta
• ???µ???se t?????sa ??d?s? (pa?????ta? ??a)
• ??t?se ??e? t?? e?d?se??
• Ta ???aµe µe????? d?a??????? B-tree µe
• O(N/B) ???? N ? a???µ?? p???e?? e??µ???s??
• -- ??st?? e??µ???s?? ?a? ?????? e??t?s??.

55
?p????? ???s????s?

• ??????? t??p?? µetat??p?? t?? B-tree se µe?????
  d?a??????? d?µ?
• a?t???a?e d?µ? se ???e p????
• d?at???se ß????t??? d?µ? p??sp??as?? e?d?se??
  (B-tree)
• ??a??p???t????
  ?????? e??t?s?? a?? ??d?s?, a???
• O(N/B) ?????? I/O e??µ???s??
• O(N2/B) ?????

56
??a??????? B-tree

• ?a st???e?a ef?d?????ta? µe d??st?µa ?pa????
  ?a? ap????e???ta? se µ?a d?µ?
• ??a??????? B-tree µe pa??µet?? b (gt16)
• ?ate?????µe?? ???f?µa
• ?? ??µß?? pe??????? st???e?a ef?d?asµ??a µe
  d??st?µa ?pa????
• ???e ??????? st??µ? t, ?? ??µß?? µe st???e?a
  e?e??? t? ??????? st?µ? t s??µat????? B-tree µe
  pa??µet?? f????? ?a? ßa?µ? e??d?? b
• B-tree µe ????t???t?ta f????? b ?a? ßa?µ? e??d??
  b se ??µß? ßa?µ?? e?s?d?? 0
• ?
• ??? bB
• ?????? e??t?s??
  I/Os

57
??a??????? B-tree ???µe??se??

• ???µe??se?? ?p?? ?a? st? B-tree
• G?a d?at???s? ??aµµ???? ????? d?at????µe t?? e???
  s??????
• ??a? ???? ??µß?? pe????e? µeta?? 3?/8 ?a?
  e?e??? st???e?a ?a? ?a???a a?e?e???.

58
??a??????? B-tree - ???es?

• ???e ??a s?et??? f???? u ?a? ???ese ??? st???e??
• ??? ? u pe????e? B1 st???e?a Block overflow
• Version split
• S?µe??se u a?e?e??? ?a? d?µ??????se ??? ??µß? u
  
• If Strong overflow
• If Strong underflow
• If t?te e??µ???se
  parent(u)
• ?????a?e a?af??? se u ?a? ???ese se u

59
Persistent B-tree ???es?

• Strong overflow ( )
• ???spase v se v ?a? v µe st???e?a (
  )
• ???µ???se parent(v)
• ?????a?e a?af??? se v ?a? ???ese a?af???? se v
  ?a? v
• Strong underflow ( )
• S?????e?se x st???e?a µe y e?e??? st???e?a ap?
  version split st? sibling (
  )
• ??? t?te (strong overflow)
  d??spase se ??µß??? µe (xy)/2 elements (
  
  )
• ??ad??µ??? e??µ???se parent(u) ?????a?e d??,
  ???ese µ?a/d?? a?af????

60
Persistent B-tree ??a??af?

• ???e ??a f???? u ?a? µa?????se st???e?? a?e?e???
• ??? u pe????e? e?e??? st???e?a
  Block underflow
• Version split
• S?µe??se u a?e?e??? ?a? d?µ??????se ??µß? u µe
  x e?e??? st???e?a
• Strong underflow ( )
• S?????e?se (version split) ?a? d??spase (strong
  overflow)
• ??ad??µ??? e??µ???se parent(u)
• ?????a?e d?? a?af????, ???ese µ?a ? d??

61
Persistent B-tree
62
Persistent B-tree A????s?

• ???µ???s?
• ????µ? ?a? epa?a????s? se ??a µ???p?t?
• ????? O(N/B)
• t??????st?? e??µe??se?? st? f???? se
  d??st?µa ?pa????
• ?ta? t? u a?e?e???
• ?? p??? d?? ???? ??µß?? d?µ????????ta?
• ?? p??? ??a block over/underflow ??a ep?ped? ???
  (in parent(l))
• ?
• Se N e??µe??se??, d?µ???????µe
• f???a
• ??µß??? i ep?peda ???
• ? blocks

63
Persistent B-tree

• ??a??????? B-tree
• e??µ???se t?????sa ??d?s?
• ??t?se ??e? t?? e?d?se??
• ?p?d?t??? ???p???s? µe ???s? existence intervals
• Standard te?????
• ?
• ?at? t? d????e?a N p???e??
• O(N/B) ?????
• ?????? e??µ???s??
• ?????? e??t?s??

64
???e? B-tree ?a?a??a???

• Level balanced B -trees
• Global instead of local balancing strategy
• Whole subtrees rebuilt when too many nodes on a
  level
• Used when parent pointers and divide/merge
  operations needed
• String B -trees
• Used to maintain and search (variable length)
  strings

65
B-tree ??µ?s?

• St?? ????a µ??µ? µp????µe ?a d?at????µe N
  st???e?a se O(N log N) ????? ???s?µ?p????ta? ??a
  ????sµ??? d??t??
• ???ese ??a ta st???e?a ??a p??? ??a all elements
  (construct tree)
• ?a???s?ase ta st?? ???d? se d?ateta?µ??? se???
  ???s?µ?p????ta? in-order d?ap??as?
• ? ?d??? a??????µ?? µe B-tree apa?te?
  I/Os
• ?? ß??t?st? ?at? ??a pa?????ta
• ?p????µe ?a ?t?s??µe B-tree ap? ??t? p??? ta ???
  se ?/?s
• Ta µa? e?d??fe?e ? ???s? d?µ?? µe
  ?/? ??st?? a?? p???? ? ??s? Buffer Tree

66
Buffer-tree ?e?????
67
?as???? ?d?e? (1)

• ???sµ??
• B-tree µe ßa?µ? e??d?? ?a? µ??e??? f????? B
  
• ???e??? M buffer se ???e es?te???? ??µß?
• ???µe??se??
• ???s???? time-stamp ??a ???es?/d?a??af? st???e???
  
• S?????? B st???e??? st? µ??µ? p??? t?? ???es? st?
  root buffer
• ??a?µat?p???se buffer-emptying ?ta? ?eµ?se? ?
  buffer

68
?as???? ?d?e? (2)

• ?a?at???s?
• ? buffer µp??e? ?a e??a? µe?a??te??? t?? m ?at?
  t? d????e?a t?? a?ad??µ???? buffer-emptying
• ?a st???e?a ?ata??µ??ta? se se??? d??ta???
• ? t? p??? m st???e?a ad??ta?ta st? buffer
• ?pa?a????s? ??e???eta? ?ta? ? leaf-node buffer
  ade???e?
• Leaf-node buffer-emptying p?a?µat?p??e?ta? µ???
  af?? ???? ?? p????? es?te????? ??µß?? ade??s???