Upgrade to Pro — share decks privately, control downloads, hide ads and more …

分散アルゴリズム(2)

suikwasha
November 07, 2012
210

 分散アルゴリズム(2)

自分用メモ
P20 - P26

suikwasha

November 07, 2012
Tweet

Transcript

  1. • ੩త෼ࢄ໰୊ ෼ࢄγεςϜ ∑ ʹଐ͢Δϓϩηε Pj ͱσʔλ Ij Λ࢖ ͬͯɼ֤ϓϩηε

    Pi ͕ؔ਺Λܭࢉ͢Δ໰୊ʹ͍ͭͯ • ࣍ͷ৚݅̏ͭΛຬͨ࣌͢ɼ੩త෼ࢄ໰୊ͱ͍͏ɽ 1.෼ࢄγεςϜͷτϙϩδʔ͸มԽ͠ͳ͍ɽ 2.෼ࢄγεςϜ͸৴པग़དྷΔʢނো͠ͳ͍ʣ 3.෼ࢄγεςϜʹ஝ੵ͞Ε͍ͯΔσʔλI͸มԽ͠ͳ͍ɽ
  2. • Ϧʔμʔબڍ໰୊ ໰୊Λղܾ͢ΔͨΊʹಛผͳϓϩηεΛબग़͢Δɽ • ֤ϓϩηε Pi ͕ม਺ vi Λ࣋ͭͱԾఆ͢Δɽ͋ΔΠϯ σοΫε

    a ( 1 <= a <= n ) ʹରͯ͠ Pa ͷม਺ va ͷ஋͸ 1 Ͱ͋Γɼͦͷଞͷ i (i != a) ʹରͯ͠͸ɼ0 Ͱ͋ΔΑ͏ ʹ֤ϓϩηε vi ͷ஋ΛηοτͤΑɽ “࠷େͷࣝผࢠΛ࣋ͭϓϩηε”ΛϦʔμʔͱ͢Δͱܾ Ί͓͚ͯ͹ɼ࠷େ஋ൃݟ໰୊ʹؼணͰ͖Δɽ
  3. • ࠷େ஋ൃݟ໰୊ ֤ϓϩηε Pj ͕૬ҟͳΔਖ਼ͷ੔਺ Ij Λσʔλͱͯ࣋͠ ͭͱ͢Δɽ͜ͷ࣌ɼ֤ϓϩηε Pi ʹ͓͍ͯɼ

    ΛܭࢉͤΑɽͨͩ͠ɼ֤ Ij ͸ O(log n) ϏοτͰදݱ͞ Ε͍ͯΔͱ͢Δɽ O(log n)ͷ੍ݶΛઃ͚Δ͜ͱͰɼ੍໿Լͷϝοηʔδෳࡶ౓Λઌʹܭࢉ͠ɼ࣍ʹ੍໿ͷͳ͍ϝοηʔδෳࡶ౓ ΛٻΊΔ͜ͱ͕ग़དྷΔʁ f (⌃ , I ) = max { Ij |1  j  n }
  4. P1 P2 P3 P4 P5 P6 P1 P2 P3 P4

    P5 P6 ૒ํ޲Ϧϯά ୯ํ޲Ϧϯά
  5. • ඇಉظ୯ํ޲Ϧϯά ୯ํ޲ϦϯάɼඇಉظγεςϜͰͷ࠷େ஋ൃݟ໰୊ɽ • ΞϧΰϦζϜ NAIVE 1. ϓϩηε͸ىಈͨ͠Βࣗ෼ͷ஋Λྡʹૹ৴͢Δɽ 2. ྡͷϓϩηε͔Βड৴ͨ͠஋Λͦͷ··సૹ͢Δɽ

    3. ৗ࣌ɼϓϩηε͸ड৴ͨ͠஋ͷ࠷େ஋ΛهԱ͢Δɽ 4. શ෦ͷ஋͕ϦϯάΛ̍ि͢Δͱϓϩηε͸࠷େ஋Λൃ ݟ͢Δɽࣗ෼ͷ஋Λ΋͏Ұ౓ड͚औΔͱఀࢭ͢Δɽ ϝοηʔδෳࡶ౓͸ɼ֤ Ij ͕ͦΕͧΕ n ճૹ৴͞ ΕΔ͔Βɼn^2 ʹͳΔɽ
  6. P1 P2 P3 P4 P5 P6 (2) (4) (8) (3)

    (5) (6) ࢝ಈϓϩηε ࠷େ஋ ॳظ஋͸ Ij (ద౰)
  7. P1 P2 P3 P4 P5 P6 (2) (4) (8) (3)

    (5) (6) ϝοηʔδΛૹ৴ ࠷ॳ͸ࣗ෼ͷ஋ [2]
  8. P1 P2 P3 P4 P5 P6 (2) (4) (8) (3)

    (5) (6) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [4][2]
  9. P1 P2 P3 P4 P5 P6 (2) (4) (8) (3)

    (5) (6) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [8][4][2]
  10. P1 P2 P3 P4 P5 P6 (2) (4) (8) (8)

    (5) (6) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [3][8][4][2] P3͔Βͷ஋͕ 8 Ͱ 3 ΑΓେ ͖͍ͨΊ࠷େ஋Λߋ৽
  11. P1 P2 P3 P4 P5 P6 (2) (4) (8) (8)

    (8) (6) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [5][3][8][4][2] P4 ͔Βͷ஋ ͕ 8 Ͱ 5 ΑΓେ͖͍ͨΊ࠷େ ஋Λߋ৽
  12. P1 P2 P3 P4 P5 P6 (2) (4) (8) (8)

    (8) (8) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [6][5][3][8][4][2] P5 ͔Βͷ஋͕ 8 Ͱ 6 Α Γେ͖͍ͨΊ࠷େ஋Λߋ৽
  13. P1 P2 P3 P4 P5 P6 (8) (4) (8) (8)

    (8) (8) ϝοηʔδΛૹ৴ ࣗ෼ͷ஋ʴड৴ͨ͠஋ [6][5][3][8] P1 ͔Βͷ஋͕ 8 Ͱ 4 Α Γେ͖͍ͨΊ࠷େ஋Λߋ৽ ఀࢭ P2͸ड৴ͨ͠ϝοηʔδྻʹࣗ෼ͷ஋(4)ؚ͕·ΕΔͨΊఀࢭ͢Δ ఀࢭ ࣍ͷϓϩηε΋ಉ༷ʹ
  14. P1 P2 P3 P4 P5 P6 (8) (4) (8) (8)

    (8) (8) ఀࢭ P3͸ड৴ͨ͠ϝοηʔδྻʹࣗ෼ͷ஋(8)ؚ͕·ΕΔͨΊఀࢭ͢Δ ఀࢭ [6][5][3] ఀࢭ
  15. P1 P2 P3 P4 P5 P6 (8) (4) (8) (8)

    (8) (8) ఀࢭ P4͸ड৴ͨ͠ϝοηʔδྻʹࣗ෼ͷ஋(3)ؚ͕·ΕΔͨΊఀࢭ͢Δ ఀࢭ [6][5] ఀࢭ ఀࢭ
  16. P1 P2 P3 P4 P5 P6 (8) (4) (8) (8)

    (8) (8) ఀࢭ P5͸ड৴ͨ͠ϝοηʔδྻʹࣗ෼ͷ஋(5)ؚ͕·ΕΔͨΊఀࢭ͢Δ ఀࢭ [6] ఀࢭ ఀࢭ ఀࢭ
  17. P1 P2 P3 P4 P5 P6 (8) (4) (8) (8)

    (8) (8) ఀࢭ P6͸ड৴ͨ͠ϝοηʔδྻʹࣗ෼ͷ஋(6)ؚ͕·ΕΔͨΊఀࢭ͢Δ ఀࢭ ఀࢭ ఀࢭ ఀࢭ ఀࢭ ͢΂ͯͷϓϩηε͕࠷େ஋8Λൃݟ͠ఀࢭͨ͠ɽ