?ata?e?

1
13

• ?ata?e?µat?sµ??

• S??a?t?se?? ?ata?e?µat?sµ??
• ???aµ???? ?ata?e?µat?sµ??
• ?pe?tat?? ?ata?e?µat?sµ??
• ???et???? ?ata?e?µat?sµ?? µe ?e?????sµ???
  ?at?????
• G?aµµ???? ?ata?e?µat?sµ??

2
?ef??a?? 13 ?ata?e?µat?sµ??
??sa????

• ???a?a a??e?a ? ?µesa (random, direct)
• e?t?p??eta? ? ??t??µe?? e???af? µe ???e?
  p??spe??se?? (?s?? ?a? µ??? µ?a),
• ???s?µ?p?????ta? ??a on-line efa?µ????,
• de? p??sf????ta? ??a se???a?? a???t?s?
  ta????µ?µ???? e???af?? ? ??a a?a??t?se??
  d?ast?µat??.
• ?e a??eß???? µetas??µat?sµ? st?? t?µ? t??
  ??e?d??? p????pte? ? ap???t? d?e????s? t??
  e???af??.
• ? ap???t? d?e????s? ap?te?e?ta? ap? t?? t???da
• a???µ?? ?????d???,
• a???µ?? at???t??, ?a?
• a???µ?? e???af??.

3
?ef??a?? 13 ?ata?e?µat?sµ??
??sa????

• ????? (dense) ???µ????ta? ta ??e?d?? µe
  s??e??µe?e? t?µ??
• p?. ??a ??e?d?? ap? 1 ??? 1000, ? i-?st? e???af?
  ?a ap????e?eta? st?? (i-1)-?st? se??da (a? ?
  ????t???t?ta µ?a? se??da? e??a? µ?a e???af?),
• p?. ??a ??e?d?? ap? 14.001 ??? 16.000, afa??e?ta?
  µ?a sta?e?? t?µ? ap? t?? t?µ? t?? ??e?d???.
• ?a ??e?d?? a?t?? t?? e?d??? ?????ta?
  a?t?de??t?d?-t??µe?a (self-indexed).

4
?ef??a?? 13 ?ata?e?µat?sµ??
??sa????

• ?ta? ta ??e?d?? de? e??a? p???? t? µe?a??te??
  µ???? t?? a??e??? e??a? ?e??.
• St?? pe??pt?s? a?t? efa?µ??eta? µetas??µat?sµ??
  t?? ??e?d??? ?ste ?a p?????e? ??a µ????te??
  d??st?µa t?µ?? d?e????se??.
• ? µ???d?? a?t? ???µ??eta? te????? d?as???p?sµ??
  ap????e?s?? (scatter storage technique) ?
  µetas??-µat?sµ?? t?? ??e?d??? se d?e????s?
  (key-to-address- transformation) ? a?????
  ?ata?e?µat?sµ?? (hashing).

5
?ef??a?? 13 ?ata?e?µat?sµ??
??sa????

• ?ta? f??t??eta? t? a??e?? desµe?eta? ????? st?
  d?s?? p?? ???µ??eta? ????a pe????? (main area).
• Se µe????? pe?????? p??ß??peta? ?a? ???s?
  pe?????? ?pe??e???s?? (overflow area).
• ?a?????ta? d?e????se?? (address factor) e??a? t?
  ???sµa t?? µe?????? t?? ????a? pe?????? p??? t?
  s??????? µ??e??? t?? a??e???.

6
?ef??a?? 13 ?ata?e?µat?sµ??
???a??se?? d??aµ???? a??e???

• ?a d??aµ??? t??a?a (dynamic random) a??e?a e??a?
  a?t? p?? µe?e?????ta? ? s??????????ta? a?????a µe
  t?? e?sa????? ?a? e?a?????.
• ???a??se?? ??a t?? ?e???sµ? a?t?? t?? a??e???
  e??a?
• ???aµ???? ?ata?e?µat?sµ?? (dynamic hashing),
• ?pe?tat?? ?ata?e?µat?sµ?? (extendible hashing),
• ???et???? ?ata?e?µat?sµ?? µe pe?????sµ???
  ?at????? (bounded index exponential hashing),
• G?aµµ???? ?ata?e?µat?sµ?? (linear hashing).

7
?ef??a?? 13 ?ata?e?µat?sµ??
???a??se?? d??aµ???? a??e???

• ?? te?????? a?t?? ???s?µ?p????? s???et???
  a??????µ??? ??a ?a apa?t?s??? st?? e??t?se??
• p?? ?a? p?te d?asp?ta? ??a? ??d??,
• p?? d?a??µ??ta? ?? e???af?? ap? t?? pa??? ??d?
  st??? ?????,
• p?? ?a? p?te s?????e???ta? d?? ??d??,
• p?? ?? e???af?? ap? t??? pa????? ??d???
  ap?d?d??ta? st? ??? ??d?.

8
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ??

• ??a s????t?s? µetas??µat??e? t?? t?µ? t??
  ??e?d??? se t?µ? d?e????s?? st? de?te?e???sa
  µ??µ? µe t??a?? t??p?
• ?ta? t? ??e?d? e??a? a???µ?t???, efa?µ??eta? ap??
  a??eß???? ??f?as?,
• ?ta? t? ??e?d? e??a? a?fa???µ?t???, efa?µ??eta?
  µetat??p? se a???µ?t??? ???s?µ?p????ta? t???
  ??d??e? ASCII, EBCDIC.

9
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ?? - ???ß??µata

• ??? ? pe??ss?te?e? t?µ?? ??e?d??? e??a? d??at??
  ?a d?s??? t?? ?d?a d?e????s?. ?? fa???µe??
  ?a?e?ta? s??????s? (collision) ?a? ?? e???af??
  s?????µe? (synonyms).
• ?ta? s?µa?t???? a???µ?? e???af?? s???st????ta?
  st?? ?d?a pe????? t?? a??e??? t?te ????µe
  p??te???sa s?????t??s? (primary clustering).
• ?at? t?? a????? p??ß?e?? desµe?eta? pe??ss?te???
  ????? ??a t? a??e??.

10
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ?? - ?a?ade??µata

• ?st? ?t? ?? 31 p?? s?????sµ??e? a??????? ???e??
  (and, or, not, the, ??p.) ap????e???ta? se ??a
  p??a?a
• t? s????? t?? d??at?? t?p??et?se?? e??a? 1050,
  e?? ?? ß?????? t?p??et?se?? (????? s??????s?)
  e??a? µ??? 1043,
• ??a a?t?st???e? µ?a ß????? t?p???t?s? st?? d??a
  e?at?µµ???a pe??pt?se??.
• ?? de?te?? pa??de??µa e??a? t? ?e??µe?? pa??d???
  t?? ?e?e????? (birthday paradox)
• ?st? ?t? ep??????ta? t??a?a ap? t? p????? 23
  ?t?µa,
• ? p??a??t?ta t??????st? d?? ?t?µa ap? t? s?????
  t?? 23 at?µ?? ?a ????? t?? ?d?a µ??a ?e?????a
  e??a? 50.83.

11
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??

• ?? n e???af?? p??pe? ?a ap????e????? se m ??se??,
  t?te ? a???µ?? t?? d??at?? t?p??et?se?? e??a? mn.
  
• ??a pa??de??µa, a? n4 ?a? m5, t?te ? a???µ??
  t?? t?p??et?se?? e??a? 625.
• ?? ß?????? t?p??et?se?? (1 p??sp??as?) e??a?
  m!/(mn)!
• st? pa??de??µa, m!/(mn)! 120.

12
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??

• ?e???te?? pe??pt?s?
• ??e? ?? e???af?? ?a a?t?st?????? se µ?a ??s?.
• st? pa??de??µa, ?a? ?? 4 e???af?? ?a a?t?st??????
  se 1 ??s?
• ?pa?t??µe?e? p??spe??se?? (n1)/2.
• st? pa??de??µa, 2,5 p??spe??se?? ?at? µ?s? ???.
• ? a???µ?? t?? d?sµe??? pe??pt?se?? e??a? m.
• st? pa??de??µa e??a? 5.

13
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??

• ?? ?p????pe? t?p??et?se?? d?a??????ta? se
  s??????se?? ap? 2 ??? n1 e???af??.
• st? pa??de??µa, ?? ?p????pe? 500 t?p??et?se??
  d?a??????ta? se t??a e?d?
• µ?a s??????s? 2 e???af??,
• d?? s??????se?? 2 e???af??, ?a?
• µ?a s??????s? 3 e???af??.

14
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??

• H p??a??t?ta µ?a? ß?????? t?p???t?s?? e??a?
• st? pa??de??µa, ??a n4 ?a? m5, p00.192.

• H p??a??t?ta t?? p?? d?sµe???? t?p???t?s? e??a?
• st? pa??de??µa, ??a n4 ?a? m5, pmax0.008.

15
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??
16
?ef??a?? 13 ?ata?e?µat?sµ??
???te??p???s? s??????se??

• ???e?e? (perfect) s??a?t?se?? ?ata?e?µat?sµ??
  ???µ????ta? a?t?? p?? de? pa?????? s?????µa.
• ???s?µ?p?????ta? µ??? se µ?????? p??a?e? t??
  ????a? µ??µ?? ??a e?d???? efa?µ???? ?p??
• µetaf?ast?? ??a ap????e?s? de?sµe?µ???? ???e??,
• epe?e??as?a f?s???? ???ssa? ??a f??t????sµa
  ???e?? ?????? s????t?ta?.
• ?????st? (minimal) ???µ??eta? ? s????t?s? p??
  desµe?e? t?? e????st? d??at? ????.
• G?a pe??pt?se?? ????d?? stat????/d??aµ????
  a??e??? (p?. a??e?a µ??a??? a?a??t?s??) ??e?
  p??ta?e? µ?a ???s? µe??d?? p?? ???eta? e??te?????
  (external) t??e??? ?ata?e?µat?sµ??.

17
?ef??a?? 13 ?ata?e?µat?sµ??
?a?????ta? f??t?s??

• ? ????? t?? ?ate???µµ???? ??se?? p??? t? s?????
  t?? ??se?? t?? a??e??? ???µ??eta? pa?????ta?
  f??t?s?? (load factor) ?a? ?s??ta?
• bkm e??a? ? a???µ?? t?? ??d?? st?? ????a pe?????,
  ?a?
• Bkfr e??a? ? pa?????ta? ?ad?p???s?? (bucket
  factor), d??ad? ? a???µ?? t?? e???af?? a?? ??d?.

18
?ef??a?? 13 ?ata?e?µat?sµ??
?a?????ta? f??t?s??

• ?s? µ????te??? e??a? ? pa?????ta? f??t?s??, t?s?
  µ????te?? e??a? ? p??a??t?ta s??????s?? ?a? t?
  a?t?st??f?.
• ? s?ed?ast?? a??e??? e??a? ?pe?????? ??a ?a ß?e?
  t?? ?s????p?a µeta?? t?? s??????se?? ?a? t??
  p?s?st?? a???s?µ?p???t?? ????? t?? a??e???.

19
?ef??a?? 13 ?ata?e?µat?sµ??
?pe??e???s?

• ?pe??e???s? (overflow) s?µßa??e? ?ta? µ?a e???af?
  p??pe? ?a ap????e??e? se ??a p???? ??d?. ??te ?
  e???af? ?ate????eta? ??a ap????e?s? se ?????
  ??d?.
• ?s? µe?a??te??? e??a? ? ??d??, t?s? µ????te??
  e??a? ? p??a??t?ta ?a ?p???e? ?pe??e???s?.
• ?s? µe?a??te?? e??a? t? µ??e??? t?? ??d??, t?s?
  p?? ?????ß??a e??a? ? p??sp??as? st? d?s??.

20
?ef??a?? 13 ?ata?e?µat?sµ??
?pe??e???s?

• ??s? p?s?st? ?pe??e???s?? a??e??? µe 200 ??d???.

21
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ??

• ??a??es? µe p??t? a???µ? (prime number division).
  ? t?µ? t?? d?e????s??, ?p?? ?a ap????e??e? ?
  e???af?, ?s??ta? µe t? ?p????p? t?? d?a??es?? t??
  t?µ?? t?? ??e?d??? d?a t?? µe?????? t?? a??e???.
• ?? s??????se?? e?a??st?p?????ta? a? d?a???t??
  e??a? ? µe?a??te??? p??t?? a???µ?? p?? e??a?
  µ????te??? ap? t? µ??e??? t?? a??e???.
• ?st? ?t? d??eta? µ?a e???af? µe ??e?d? 172.148
  ??a ?a ap????e??e? se a??e?? µe 7000 ??d???.
  ?s??e? 172148 mod 6997 4220

22
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ??

• ?etat??p? ???a? (radix conversion). Te??e?ta? ?t?
  ? t?µ? t?? ??e?d??? de? e??a? a???µ?? t??
  de?ad???? s?st?µat?? ?a? ep?µ???? p??pe? ?a
  µetat?ape? se a???µ? t?? s?st?µat?? a?t??.
• ?ts? a? ?p?te?e? ?t? ? s???e???µ???? a???µ?? ??e?
  ?? ß?s? t? 11, t?te µe t? µetat??p? p????pte?
• 1x115 7x114 2x113 1x112 4x11 8
  266373
• ?? ap?t??esµa ?a??????p??e?ta? d?a????ta? µe
  6997.
• ? d?e????s? t?? ??d?? t?? a??e??? ?s??ta? µe 487.

23
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ??

• ??s? t?? tet?a????? (mid square). ?aµß????ta? ta
  µesa?a ??f?a t?? tet?a????? t?? t?µ?? t??
  ??e?d???.
• St? pa??de??µa, a? ? s???e???µ??? t?µ? t??
  ??e?d??? ????e? st? tet??????, p????pte?
  029634933904.
• ?aµß????ta? ta 4 µesa?a ??f?a, d??ad? 3493.
• ???????e? ?a??????p???s? ?? p??? t? 7000, ?p?te
  34937000/99992445.

24
?ef??a?? 13 ?ata?e?µat?sµ??
S??a?t?se?? ?ata?e?µat?sµ??

• ?eta????s? (move) ? ??p??s? (fold). ? t?µ? t??
  ??e?d??? ?????eta? se d?? tµ?µata p??
  p??st??e?ta?.
• d??eta? ? a???µ?? 17207359 p?? ?????eta? se d??
  tet?a??f???? a???µ???, t??? 1720 ?a? 7359.
• S?µf??a µe t?? p??t? µ???d? (µeta????s?)
• ???eta? p??s?es? ?a? p????pte? 9079,
• a??????e? ?a??????p???s? ?? p??? t? µ??e??? t??
  a??e??? 90797000/19.998 3178.
• S?µf??a µe t? de?te?? µ???d? (d?p??s?)
• p??st??e?ta? ?? a???µ??, af?? p??ta ? se??? t??
  ??f??? t?? de?te??? a???µ?? a?t?st?afe?
  1720953711257,
• a??????e? ?a??????p???s? 11.257 7000/19.998
  3940.

25
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ? d??aµ???? ?ata?e?µat?sµ?? ?ta? ? p??t? ???????
  d?µ? d??aµ???? t??a??? a??e??? p?? eµfa??s???e
  st? ß?ß?????af?a.
• ? e?e???t?? p?? t?? pa???s?ase, ? Larson
  ?e??e?ta? ap? t??? ?eµe???t?? t?? pe?????? a?t??.
  
• ? d??aµ???? ?ata?e?µat?sµ?? ap?te?e?ta? ap? d??
  f?s??? a?e???t?te? d?µ?? ??a? ?at????? ?a? ??a
  ????? a??e??.

26
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ? ?at?????? e??a? ??a d?s?? d?ad???? d??d??? p??
  ???p?????ta? ?? s??dedeµ??e? d?µ?? st?? ????a
  µ??µ?.
• St? te?e?ta?? ep?ped? t?? d?ad???? d??d???
  pe?????-?ta? de??te? p??? t?? se??de? t?? ??????
  a??e??? p?? ß?ßa?a e??a? ap????e?µ??? st?
  de?te?e???sa µ??µ?.
• ? a???µ?? t?? d?ad???? d??d??? p?? ap?te???? t?
  d?s?? ?s??ta? µe t?? a???µ? t?? ??d??, bk.
• ??a s????t?s? ?ata?e?µat?sµ??
• h(key) key mod bk
• d??e? t? d?ad??? d??d??, ?p?? ß??s?eta? ? ??d??
  p?? pe????e? t?? e???af?.

27
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ???e ??d?? ??e? ????t???t?ta Bkfr e???af??.
• ?at? t?? e?sa???? t?? (Bkfr1)-?st?? e???af??
  ???eta? d??spas? ??d?? ??a ?a t?? de??e?.
• ?? s?st?µa pa?a???e? ??a ??? ??d? ?a? ?? (Bkfr1)
  e???af?? a?ad?a??µ??ta? µeta?? t?? d?? ??d??.
• ???s?µ?p??e?ta? µ?a de?te?? s????t?s? h2(key) p??
  µe sp??? t? ??e?d? pa???e? µ?a ?e?d?t??a?a
  d?ad??? s?µß???se??? ?p????d?p?te µ?????, ?p?? ta
  0 ?a? 1 eµfa?????ta? ?s?p??a?a.
• ?? t? p??t? bit e??a? 0 (a?t?st???a, 1), t?te ?
  e???af? ?ate????eta? st?? pa?a?? (a?t?st???a, st?
  ???) ??d?.

28
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ?????? ?a???a ap? ta bk d?ad??? d??d?a t?? d?s???
  ap?te?e?ta? µ??? ap? µ?a ???a, ?p?te ? ?at??????
  ??e? µ??? ??a ep?ped?.
• ?ta? ???e? ??p??a d??spas? ??d??, t?te p??pe? t?
  a?t?st???? d??d?? ?a epe?ta?e? ?at? ??a ep?ped?.
• ?p? t? ???a t?? a?t?st????? d??d???
  d?µ????????ta? d?? ap?????? e??te????? ??µß?? µe
  t??? a?t?st?????? de??te? p??? t??? d?? ??d???.
• ? a??ste??? ??µß?? de???e? st?? ?p?????ta ??d?,
  e?? ? de???? ??µß?? de???e? st? ??? ??d?.

29
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ?? t?p?? t?? es?te?????-e??te????? ??µß?? e??a?
  d?af??et????.
• ?? es?te????? ??µß?? ap?te????ta? ap? ta e???
  ped?a
• s?µa?a (t?µ? 0),
• de?d????? de??t?? p??? t?? pat??a ??µß?,
• de?d????? de??t?? p??? t?? a??ste?? ap?????, ?a?
• de?d????? de??t?? p??? t?? de??? ap?????.
• ?? e??te????? ??µß?? ap?te????ta? ap? ta e???
  ped?a
• s?µa?a (t?µ? 1),
• de?d????? de??t?? p??? t?? pat??a ??µß?,
• de??t?? p??? t?? ??d? t?? a??e???, ?a?
• µet??t?? t?? ap????e?µ???? e???af?? st?? ??d?.

30
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ?? - ?a??de??µa

• ?st? ?t? se ?e?? a??e?? d??aµ???? ?ata?e?µat?sµ??
  µe ??d??? µe?????? d?? e???af?? p???e?ta? ?a
  e?sa????? d?ad????? e???af?? µe t?µ?? ??e?d???
• 4, 5, 10, 12, 19, 52, 56, 72 ?a? 90.
• ?????? t? a??e?? s?ed???eta? ?ste ?a ??e? 3
  ??d???.
• O? p??t? s????t?s? ?ata?e?µat?sµ??
  ???s?µ?p??-e?ta? ? s????t?s? h1(key) key mod 3,
  p?? ?????e? t? d?s?? t?? ?ata????? se 3 d?a???t?
  d?ad??? d??d?a.
• O? de?te?? s????t?s? ep????eta? ? s????t?s? key
  mod 10, ?ste ap? t? ??e?d? ?a p?????e? ?p????p?
  ap? 0 ?? 9.

31
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ???e t?µ? t?? ?p????p?? ?e??e?ta? ?? sp???? se
  µ?a ?e?d?t??a?a ?e???t??a, R(), p?? pa???e?
  d?ad??? ??f?a 0 ?a? 1 µe t?? ?d?a p??a??t?ta
  (d??ad? 50).
• ?? ap?t??esµa µ?a? t?t??a? ?e???t??a? ??a ???e
  sp??? fa??eta? st?? p??a?a

R(0) R(1) R(2) R(3) R(4) R(5) R(6) R(7) R(8) R(9)
1011 0000 0100 0110 1111 0101 0001 1110 1001 0011
32
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• ?? te???? ap?t??esµa t?? e?sa????? t?? 9 e???af??
  µe t? d?µ??????a t?? ?ata????? t?? 3 d??d??? ?a?
  t?? a??e??? t?? 5 ??d?? e??a? t? e???.

33
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ??

• St? p??????µe?? pa??de??µa apa?te?ta? 1 µ???
  p??sp??as? st? d?s?? ??a ep?t??? a?a??t?s?.
• ?at? t?? a?a??t?s? µ? ?p?????t?? ??e?d??? µp??e?
  ?a ß?e?e? e??te????? ??µß?? µe µet??t? e???af??
  ?s? µe 0.
• ??a?t?a? t?? d?ad?????? e?sa????? ? ?at??????
  a????e? ?a? tµ?µa t?? ?a p??pe? ?a ap????e?te?
  st? de?te?e???sa µ??µ?, ?p?te apa?t???ta? 2
  p??spe??se?? st?? ep?t??? a?a??t?s?.
• H µ?s? t?µ? t?? pa?????ta ???s?µ?p???s?? ?????
  e??a? 69 (?p?? ?a? sta ?-d??d?a).

34
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ?? - ?a?a??a??

• ?e????? a?aß??? d??spas?? (deferred splitting).
• ?e? ???eta? d??spas? t?? ??d?? ?ta? sa?t??
  ?ate?-????e? ? (Bkfr1)-?st? e???af?, a???
  d?µ?????e?ta? a??s?da ?pe??e???s?? µe ??a de?te??
  ??d?.
• ?? ?e???? a?t? t?? ??d?? ?a d?aspas?e? ?a? ?
  ?at?????? ?a e??µe???e? ?ta? ?a ????? e?sa??e?
  ß Bkfr e???af??, ?p?? 1?ß?2.
• ?? p?e????t?µa e??a? ?t? ? ?at?????? ?a e??a?
  µ????-te??? ?at? ß f???? ?a? ?a ???? st?? ????a
  µ??µ?.

35
?ef??a?? 13 ?ata?e?µat?sµ??
???aµ???? ?ata?e?µat?sµ?? - ?a?a??a??

• ?? t? a??e?? µe?a??se? ?pe?ß?????, t?te µp??e?
  d????ta? st? ß µe?a??te?e? t?µ?? ?a ep?t?ap???
  a??s?de? ?pe??e???s?? µe?a??te??? µ?????, ?ste ?
  ?at?????? ?a ???? ?p?sd?p?te st?? ????a µ??µ?.
• St? ?e???te?? pe??pt?s? ?a ?????? ?ß?
  p??spe??se?? st? d?s??.

36
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• H d?µ? a?t? p??t????e ap? t??? Fagin et al. ?a?
  ?ta? ? ??????? de?te?? ???p???s? d??aµ????
  t??a??? a??e???.
• ? a????????a t?? µetas??µat?sµ?? t?? ??e?d??? p??
  e?te????ta? st?? epe?tat? ?ata?e?µat?sµ? ??e? ??
  e???

37
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? p??t?? µetas??µat?sµ?? e??a? µ?a s????t?s?
  ?ata?e?µat?sµ?? p?? ape??????e? ?at? t??a?? t??p?
  ??a d??st?µa ??e?d??? se ??a sta?e?? d??st?µa
  d?e????se??
• ? pe?????sµ?? e??a? ?t? t? d??st?µa d?e????se??
  p??pe? ?a e??a? d??aµ? t?? d??,
• p??t?µ?ta? ?a e??a? p??t?? a???µ??, ??' a?t?
  ep????eta? ? µe?a??te??? a???a??? p?? e??a?
  aµ?s?? µ????te??? ap? t? d?ad??? d??aµ?.
• ??a pa??de??µa, ? µe?a??te??? p??t?? a???µ?? p??
  e??a? µ????te??? ap? t? 216 e??a? ? 65521.

38
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• St? s????e?a ? t?µ? t?? ??e?d??? µetat??peta?
  st?? ?s?d??aµ? d?ad??? a???µ? ?a? ?aµß????ta? ta
  p??ta ??f?a t??. ???a? d??at?? ?a µ? ??f???? ta
  p??ta bits a??? ta te?e?ta?a ? ??p??a µesa?a.
• ?a bits a?t? ?aµß????ta? ?? e?s?d?? se ?at?????,
  p?? pe????e? de??te? p??? t??? ??d??? t??
  a??e???.

39
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? ?at?????? a?t?? e??a? ??a? µ???d??stat??
  p??a?a? µe 2d st???e?a, ?p?? d e??a? ? a???µ??
  t?? ep??e??-µe??? ??f???, ?a? ???eta? ß????
  (depth) ? ep?ped? (level) t?? ?ata?????.
• ? a???µ?? t?? ??f??? p?? e?????ta? ap? t?
  ap?t??e-sµa t?? s????t?s?? ?ata?e?µat?sµ??
  µetaß???eta? ??????? a?????a µe t? µetaß??? t??
  µe?????? t?? a??e???.

40
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ?? - ?a??de??µa
???s?µ?p?????ta? ta p??ta t??a ??f?a t??
µetas??µat?sµ??. ? p??a?a? ap?te?e?ta? ap? 8
de??te? p?? a?af????ta? se 8 t? p??? ??d???.
41
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ?? - ?a??de??µa

• ?st? ?t? ? d?ad??? µ??f? t?? µetas??µat?sµ?? e???
  ??e?d??? e??a? 0110100101100101. ?p? a?t?? t??
  a???µ? ap?µ??????ta? ta 3 p??ta bits (011) p??
  ?s?d??aµ??? µe t? de?ad??? a???µ? 3.
• ?e p??sp??as? st?? ?p' a???µ? 3 e?s?d? t?? p??a?a
  ß??s?eta? ? ?at??????? de??t?? p?? a?af??eta?
  st?? ??d? G.

42
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ???e ??d?? s???de?eta? ap? µ?a pa??µet?? d', p??
  ???eta? ß???? (depth) ? ep?ped? (level) t??
  ??d??.
• ?? ß???? d????e? t?? a???µ? t?? bits p?? e??a?
  ?????? ??a ta ??e?d?? ???? t?? e???af?? t?? ??d??
  ?a? e??a? d??d.
• O a???µ?? t?? de??t?? p?? a?af????ta? se ??a
  ded?µ??? ??d? e??a? 2d-d'.

43
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ?a ß?µata p?? a?????????ta? st?? epe?tat?
  ?ata?e?-µat?sµ? e??a? ta e???
• efa?µ??eta? s????t?s? ?ata?e?µat?sµ?? st? ??e?d?,
• e?????ta? ta p??ta d bits,
• ???s?µ?p??e?ta? ? ?at?????? ??a t?? e?t?p?sµ? t??
  ?at??????? de??t?,
• µe ß?s? t?? de??t? ???eta? p??sp??as? st?? ??d?,
  ?a?
• ???eta? a?a??t?s? st?? ??d? ??a t?? e??es? t??
  ??e?d???.

44
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? pe??e?t???t?ta e??? ??d?? de? p??pe? ?a e??a?
  µ????te?? ap? ??a p?s?st? p?? ????eta? ap? t?
  ???st?, p.? 50.
• ? epe?e??as?a t?? e?sa????? ?a? d?a??af?? e??a?
  a??et? p???p???? d?ad??as?a.

45
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ?st? ?t? st?? ??d? ? p??pe? ?a e?sa??e? µ?a
  e???af?.

46
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ??ad??as?a e?sa????? se ?eµ?t? ??d?.
• ????a?e?ta? ep??tas? t?? a??e???.
• ???st??eta? ???? ??d??.

• ?? µ?s?? de??te? a???-???? ?a? a?af????ta? st?
  ??? ??d?, e?? µetaf????ta? ?a? ?? a?t?st???e?
  e???af??.

47
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ?ta? ? ??d?? p?? p???e?ta? ?a d?aspas?e?
  a?af??eta? µe ??a de??t?, t?te ???eta? ep??tas?
  ?ata?????.
• ? ?at?????? d?p?as???eta? µe ???e ??a e?sa????
  ?a? dd1.
• ???e de??t?? ?ata?aµß??e? t??a d?? ??se??.
• ???e ??d?? ??e? pe??ss?te???? ? d?? de??te?,
  ?p?te µp??e? ?a a???????se? d??spas?.

48
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??
49
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? ?at?????? d?p?as???eta? ???e f??? p?? d?asp?ta?
  ??a? ??d??, ??a t?? ?p??? ?s??e? ? s??s? dd',
  a?e???t?ta ap? t?? ?at?stas? t?? ????? ??d??.
• ??t? ? te????? µp??e? ?a ?d???se? se pa?????????
  ?atast?se??.

?a??de??µa e?sa????? 10 (00001010)2 142
(10001110)2
50
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• 52 (00110100)2
• 56 (00111000)2
• ?pe?d? ????? ?d?a ta p??ta 2 ??f?a ???eta?
  d?p?as?asµ?? t?? ?ata????? d?? f????.

51
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• 12(00001100)2
• 19(00010011)2
• ??p?as?asµ?? t?? ?at?-????? ???eta? ?a? µe t??
  e?sa???? t?? e???af?? µe ??e?d?? 12 ?a? 19.
• ? ?at?????? ??e? 2416 e?s?d???.
• ???et?? d?a???t?? de??te? de?????? e?te se ?e??
  e?te se ????? ??d?.

52
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ??a d?a??af? µp??e? ?a p???a??se? s???????s? t??
  a??e???.
• ? s?ss?µ?t?s? d?? ??d?? se ??a? ???eta? ?p? t?e??
  p???p???se??
• ? µ?s? pe??e?t???t?ta t?? d?? ??d?? de? ?epe???
  t? 50,
• ?? ??d?? p?? p???e?ta? ?a s??d?as????
  ?a?a?t??????ta? ap? t?? ?d?a t?µ? t?? pa?aµ?t???
  d',
• ta ??e?d?? t?? e???af?? t?? d?? ??d?? ????? ?????
  ta p??-ta (d'-1) ??f?a t?? ap?te??sµat?? t??
  µetas??µat?sµ?? ?ata?e?µat?sµ??.

53
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? p??t? p???p??es? ?s??e? ??a t??? ??d??? ?, ?.

• ?? ??d?? ?µ?? de? e??a? s?????e?s?µ?? ??at? ta
  ??e?d?? t?? e???af?? de? ????? ?d?? a???µ? ??????
  ??f???.
• ??t??eta, µp????? ?a s?????e?t??? ?? ??d?? D, E.

54
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ?ta? ???? ?? de??te? ap?te???? ?e???, t?te ?
  ?at?????? µp??e? ?a ?p?d?p?as?aste?.
• ?a??de??µa ?,?,?,?,?,?,G,G,?,?,?,?,?,?,?,?
• ?p??e? ?a ???e? ?p?d?p?as?asµ??.
• ?a??de??µa ?,?,?,?,?,?,?,G,G,?,?,?,?,?,?,?,?
• ?e? µp??e? ?a ???e? ?p?d?p?as?asµ??.

55
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• Se µ?a ap?? ???p???s? t?? ?ata????? µp??e? ?a µ??
  ?p?????? pe??tt?? de??te?.
• ?? ??a ded?µ??? ep?ped? d t?? ?ata????? ?a? ??a
  ??p??? s??d?asµ? d ??f??? de? ?p??????
  a?t?st???e? t?µ?? ??e?d???, t?te ? a?t?st?????
  de??t?? ??e? t?µ? NULL.
• ??e? ta??te?? a?ep?t??? a?a??t?s? ?a? ap???ste??
  d?ad??as?a d??spas?? ??d??.
• ??e? µe?a??te?e? apa?t?se?? ?????.

56
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ? pe??e?t???t?ta t?? ??d?? p??pe? ?a e??a? 50.
• ? p??a??t?ta ?a ???e? lt 50 e??a? µ?de???? a?
• ? a???µ?? t?? e???af?? n e??a? µe?????,
• ? ????t???t?ta t?? ??d?? e??a? ep?s?? µe????, ?a?
• ta ??e?d?? µ???????ta? ?µ???µ??fa µeta?? t??
  ??d??.
• ? µ?s? pe??e?t???t?ta t?? ??d?? e??a? 69.

• ? µ?s? t?µ? t?? a???µ?? t?? ??d?? t?? a??e???
  e??a?
• ? µ?s? t?µ? t?? a???µ?? t?? e?s?d?? t?? ?ata?????
  e??a?

57
?ef??a?? 13 ?ata?e?µat?sµ??
?pe?tat?? ?ata?e?µat?sµ??

• ?e???e?t?µata
• Se e?a??et???? pe??pt?se?? ? ?at?????? µp??e? ?a
  ???e? t?s? µe?????, ?ste ?a µ?? ???? st?? ????a
  µ??µ? (a?e???e??t?? d?p?as?asµ?? t?? ?ata?????)
• ?p?te ap????e?eta? st? de?te?e???sa µ??µ?, ?a?
• apa?t???ta? ep?p???? p??spe??se?? st? d?s??.
• ?e? p??sf??eta? ??a e??t?se?? d?ast?µat??.
• ?? ??st?? e?sa????? ??e? e???se?? p?? ?fe????ta?
  st?? p????? ?a? ta?t?????e? d?asp?se?? t?? ??d??
  t?? a??e??? ?a? t?? ?ata?????.

58
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ?p???e? ta 2 ap? ta 3 µe???e?t?µata t?? epe?tat??
  ?ata?e?µat?sµ??
• ? ?at?????? de? µp??e? ?a ?epe??se? ??a µ???st?
  µ??e??? p?? ?a?????eta? ap? t? d?a??s?µ? ????a
  µ??µ?,
• ?? se??de? t?? ?ata????? e??a? d???µe?? t?? 2 µe
  µ???st? 2max.
• ? µetas??µat?sµ?? t?? ??e?d??? a??????e? ??a?
  a???µ? ß?µ?t?? p?? ep???e? t? p??ß??µa t??
  ta?t??????? d?asp?se??.

59
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ?a ??e?d?? µetas??µat????ta? µe ß?s? µ?a
  s????t?s? ?ste ?a p?????e? µ?a ?µ???µ??f?
  ?ata??µ?.
• ?? ap?t??esµa t?? s????t?s?? a?a?ata??µeta?
  e??et??? µe ß?s? t?? t?p?
• exhash(k) 2h(k) 1
• k e??a? t? ??e?d?,
• h(k) t? ap?t??esµa t?? p??t?? µetas??µat?sµ??,
  ?a?
• exhash(k) t? ap?t??esµa t?? de?te???.

60
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ?e???? ap?t??esµa
• ?ata??µ? p?? d?a????eta? ??a t? s?ss??e?s? t??
  ??e?d??? p??? t? ??t? ???? t?? d?ast?µat?? t??
  d?e????se??.
• ?? ??d?? de? d????ta? t?? ?d?? a???µ? e???af??
  ?a? ? ep?d?s? t?? e?sa????? e??a? pe??p?? sta?e??
  se ??? t? d????e?a t?? ???? t?? a??e???.

61
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????
62
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ?a p??ta bits t?? exhash(k) ?a???????? t? se??da
  t?? ?ata?????, ?p?? e??a? ap????e?µ???? ? de??t??
  p??? t?? ?at?????? ??d?.
• ? ep????? t?? se??da? (ap? t? s????? t?? se??d??
  t?? ??d??), ?p?? ?a p??pe? ?a s??e??s?e? ?
  a?a??-t?s?, ???eta? µe ß?s? µe???? ap? ta ep?µe?a
  bits.
• Se ???e ??d? a?t?st???e? µ?a pe?????
  ?pe??e???s??, p?? e??a? ???a??µ??? ?? d?ad???
  d??d?? p?? ???µ??eta? ?-d??d??.
• ? ?at?????? ??a a?t? t? d??d?? ap????e?eta? st??
  p??t? se??da t?? a?t?st????? ??d??.
• ?at? pa??µ??? t??p?, ? d?a?e???s? t?? pe??????
  ?pe??e???s?? ???eta? µe ta ep?µe?a bits t??
  exhash(k).

63
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????
exhash(240)0011001100
exhash(641)1000101100
exhash(670)1001001011
64
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ??a??t??µe t? ??e?d? 204.
• ?s??e? exhash(204)00110011002.
• ? ?at?????? ap?te?e?ta? ap? 8 se??de?
• ?e?????ta? ta 3 p??ta bits ??a t?? p??sp??as? t??
  ?ata?????,
• ? a?a??t?s? ?ate????eta? st? 2? se??da t??
  ?ata?????,
• ? a?a??t?s? te?µat??eta? st?? ??d? ?.

65
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ??a??t??µe t? ??e?d? 641.
• ?s??e? exhash(641)1000101100.
• ? ?at?????? ap?te?e?ta? ap? 8 se??de?
• ?e?????ta? ta 3 p??ta bits ??a t?? p??sp??as? t??
  ?ata?????,
• ? a?a??t?s? ?ate????eta? st? 5? se??da t??
  ?ata?????
• ? ??d?? ??e? 8 se??de?,
• ?aµß????ta? ta ep?µe?a 3 bits ??a d?e??????s? t??
  se??da?,
• ? a?a??t?s? s??e???eta? st?? se??da ?,
• epe?d? t? 4? ?a? 5? bit 01, s??e???eta? st?
  ?-d??d??,
• apa?t???ta? 3 p??spe??se?? (st?? se??de? ?, ?, ?).

66
?ef??a?? 13 ?ata?e?µat?sµ??
???et???? ?ata?e?µat. µe pe?????sµ??? ?at?????

• ??a??t??µe t? ??e?d? 670.
• ?s??e? exhash(670)1001001011.
• ? ?at?????? ap?te?e?ta? ap? 8 se??de?
• ?e?????ta? ta 3 p??ta bits ??a t?? p??sp??as? t??
  ?ata?????,
• ? a?a??t?s? ?ate????eta? st? 5? se??da t??
  ?ata?????,
• ? ??d?? ??e? 8 se??de?,
• ?aµß????ta? ta ep?µe?a 3 bits ??a d?e??????s? t??
  se??da?,
• ? a?a??t?s? s??e???eta? st?? se??da ?,
• a? de? ?p???e?, s??e???eta? st? ?-d??d?? st??
  se??da J.

67
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ??

• ? µ???d?? t?? ??aµµ???? ?ata?e?µat?sµ?? (linear
  hashing) de? ???s?µ?p??e? ?at?????.
• ???s?µ?p??e? µe?a??te?e? a??s?de? ?pe??e???s??
  ??a ?a ep?te???e? µe?a??te?? p????t?ta t?? ??d??.
• ?? ??e?d? µetas??µat??eta? µe µ?a s????t?s?
  ?ata?e?µat?sµ??.
• ?aµß????ta? ta k te?e?ta?a d?ad??? ??f?a t??
  ap?te??sµat?? t?? µetas??µat?sµ??.

68
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ??
69
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ??

• ?? a??e?? µe?a???e? µe d?ad?????? d?asp?se??
  ??d??
• ?? e???af?? µ???????ta? st??? d?? ??d??? a?????a
  µe t?? t?µ?? t?? k1 te?e?ta??? bits.
• ???a?? t?µ? (boundary value) ???µ??eta? ? t?µ?
  p??a ap? t?? ?p??a ?? ??d?? d?a??????ta? ap? ta
  te?e?ta?a k bits.
• St?? ep??efa??da ???e a??e??? ??aµµ????
  ?ata?e?µa-t?sµ?? ap????e?eta? ? ???a?? t?µ? ?a? ?
  a?t?st???? t?µ? t?? k.
• H d?a?e???s? t?? e?sa????? ???eta? µe ß?s? t??
  ???a?? t?µ? ?a? t?? t?µ? t?? k.

70
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ??
??sa???? p??te ???? e???af?????? t??
e?sa???? ?et? t?? e?sa????
71
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??a??t?s?

• ?p?µ??????ta? ta te?e?ta?a k bits t??
  ap?te??sµat?? t?? µetas??µat?sµ??.
• ?? ? t?µ? p?? p????pte? e??a? µ????te?? t??
  ???a??? t?µ?? t?te ?aµß????ta? k1 bits.
• ? ep?d?s? t?? a?a??t?s?? se a??e?? ??aµµ????
  ?ata?e?µat?sµ?? e??a? p??? ?a?? ?a? p??se????e?
  t? µ?a p??sp??as? st? d?s??.

72
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• ??a a??e?? ap?te?e?ta? ap? 8 ??????? ??d??? µe
  ????t???t?ta 10 e???af??.
• ? pa?????ta? f??t?s?? de? p??pe? ?a ?pe?ße? t?
  70.
• ??t?? ap? t?? ????a pe????? ?p???e? ?a? ? pe?????
  ?pe??e???s??.
• Ge???? ?ta? e?s????ta? Lf Bkfr e???af??
  d?µ?????e?-ta? ??a? ???? ??d??.
• ? ?pe??e???s? de? p???a?e? apa?a?t?ta d??spas?,
  ??te ? d??spas? µe???e? apa?a?t?ta t??
  ?pe??e???s?.
• ? d??spas? t?? ??d?? e??a? ??aµµ??? ap? t?? a???
  p??? t? t???? ?s?eta ap? t? p???? ??d??
  ?pe??e????e?.

73
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• ????af?? n56.
• ?a?????ta? f??t?s?? Lf70.
• ??sa???? 7 ???? e???af??.
• ??µ??????a ???? ??d?? ?ste ?a pa?aµe??e? Lf70.

74
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• ??ad?????? e?sa?????

75
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• Se a??e?? µe Bkfr50 ?a? Lf 75 apa?t???ta? ?at?
  µ?s? ??? 2,62 p??spe??se?? st? d?s?? ??a t??
  e?sa???? µ?a? ??a? e???af??
• apa?te?ta? 1 p??sp??as? ??a ?a ???e? ?????? ??d??
  st?? ????a µ??µ?,
• ?a d?µ???????e? ??a? ???? ??d?? µe p??a??t?ta
  1/Bkfr,
• apa?t???ta? ???e? 2 p??spe??se?? st? d?s?? ??a
  t?? epa?a-ap????e?s? t?? e???af??, ?a?
• a? ? a?????? ??d?? d?a??te? ?a? a??s?da
  ?pe??e???s??, t?te ?a e??a? apa?a?t?t? ?a
  p??spe?as?e? ?a? a?t?.

76
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• ??????? ??st?? e?sa?????
• G?a Bkfr50 ?a? Lf75 ?s??e?

77
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??sa????

• ?? ??st?? e?sa????? e???af?? se a??e?? ??aµµ????
  ?ata?e?µat?sµ?? s?µpe???aµß??e? ?a? t? ??st??
  t?p???? a?ad???????s??.
• ??t??eta, st? stat??? a??e?? ?ata?e?µat?sµ?? ?
  a?ad???????s? ???eta? pe???d???.

78
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??a??af?

• ???????µ?? d?a??af??
• ?????ta? st?? ????a µ??µ? ??e? t?? e???af?? t??
  ??d?? ?a? t?? a??s?da? ?pe??e???s?? ?a?
  µetaf??eta? ? te?e?ta?a e???af? t?? a??s?da? st?
  ??s? a?t?? p?? d?a???feta?.
• ?? d?a???feta? ? e???af? p?? e??a? te?e?ta?a st??
  a??s?da, t?te ap??? e?e??e???eta? ? ?????.
• ?? ? a???µ?? t?? e???af?? t?? a??e??? ?p??e?peta?
  ?at? Bkfr e???af??, ?ste ? pa?????ta? f??t?s?? ?a
  ??e? t?? e????st? t?µ?, t?te ? te?e?ta??? ??d??
  s?????e?eta? µe t?? ??d? p?? ??e? ????? ta k
  te?e?ta?a bits.
• ??????? ??st?? d?a??af??

79
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??a??af?

• ??a??af?
• 4 e???af?? ap? t?? ??d? 010,
• 2 e???af?? ap? t?? ??d? 011,
• 1 e???af?? ap? t?? ??d? 1000.

80
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ??a?t??t??? a?????s?

• ? ??aµµ???? ?ata?e?µat?sµ?? de? d?at??e? t?? t???
  t?? ??e?d??? t?? e???af??.
• ?????? e?a?t??t???? a?????s??

81
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ?a?a??a???

• G?aµµ???? ?ata?e?µat?sµ?? µe µe????? epe?t?se??
  (linear hashing with partial expansions).
• ?ta? ? pa?????ta? ???s?µ?p???s?? ????? ?pe?ße?
  t?? p???a????sµ??? t?µ?, ?? e???af?? 2 ??d??
  a?ad?a??µ??ta? µeta?? 3 ??d??.
• ? µ???d?? a?t? ße?t???e? t?? ep?d?s? t??
  a?a??t?s?? ?a? t? ???s? t?? ????? µe t?µ?µa t?
  a???µ??? ??st?? e?sa????? se s??s? µe t?? a?????
  µ???d?.

82
?ef??a?? 13 ?ata?e?µat?sµ??
G?aµµ???? ?ata?e?µat?sµ?? ?a?a??a???

• G?aµµ???? ?ata?e?µat?sµ?? µe p??te?a??t?ta
  d??spas?? (linear hashing with priority
  splitting).
• ?? ???e? ?p??ßas? t?? ?a????sµ???? t?µ?? t??
  pa??-???ta ???s?µ?p???s?? ?????, t?te d??eta?
  p??te-?a??t?ta st? d??spas? t?? ??d?? µe t?
  µe?a??te?? a??s?da ?pe??e???s??.
• G?a t?? ???p???s? a?t?? t?? µe??d?? apa?t???ta?
  ep?p???? d?µ?? p?? ?µ?? e??a? s?et??? µ????? ?a?
  ap????e???ta? st?? ????a µ??µ?.