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Hiroaki Shiokawa

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Hiroaki Shiokawa

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Hiroaki Shiokawa

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  2. 2. Hiroaki Shiokawa h ­h Research Interests ­h c c ­h d DB w d 2011/4 2015/10 NTT 2015/11 (
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  6. 6. ­h l ­h ­h h – • • KQOBKXU • C C • GOL C C – • m – j • G – – ­ ­ 3 4 u r h h ,
  7. 7. ­h l r w - h B m k2×10% GOL m m j GOL D S]]O[k2×10& 6KMOL Uk5×10& 7 QVOk10( j m 10( h ( / ­h s v w vg
  8. 8. l C 6 ­h h – ( , g7[K R 4K]Kg – fA O[b [ MO SXQg l C5j:A5 k – ( g7[K R 1VQ [S]RW g .
  9. 9. :A5 uz l , – D + w x – – ( , , m /
  10. 10. l ­h – h x l v j k – x m • C C I J • m I J
  11. 11. l l y l y ü 9XM[OWOX]KV 1QQ[OQK]S X x ü (R K Kb X NO x ü 8 CRS UK K O] KV f6K ] 1VQ [S]RW P [ N VK[S]b LK ON 7[K R 3V ]O[SXQ g 9X [ M 1119 ( ) 8 CRS UK K O] KV fC31 0 5PPSMSOX] 1VQ [S]RW P [ 6SXNSXQ 3V ]O[ 8 L KXN ]VSO[ X K[QO MKVO 7[K R g F 42 ( +
  12. 12. l w e w s ) – y h y – )(+,) x – • x • x RW L] ?X URaNM 5] ICRS KXN KVSU D 1 9e J (
  13. 13. XM]U R l – 5 : O WKX KXN 7S[ KX f6SXNSXQ KXN O KV K]SXQ M WW XS]b ][ M] [O SX XO] [U g ,/ (, ) ( ) . = 0 122 23 − 52 23 6 2∈9 : x :
  14. 14. XM]U R b 1 * ) ( ( ( ( 1( 1 b 1 - ) * ( 1, 2 4 w r r w v 1 2
  15. 15. r l – m h x + i ( ∑ % < % <=> = 127 • h w t w w r ) ∑ ∑ % < %@< A=> %@< A % <=> = 1932
  16. 16. m m R W ?N W I J y XM]U R ,
  17. 17. l v XM]U R l XM]U R w y – SX Ka [WKVScON M ] x – D(EF) x R W ?N W H R W N U ) +I -
  18. 18. m m m R W ?N W I J ?N W I J 5? I J y N VK[S]b m m O WKX XM]U R .
  19. 19. l o h XM]U R XM]U R P RW ∆H l ∆H h l ) +I )(J log +) ?N W 5? ∆.2A = 2{2312A − 525A} N VK[S]b QKSX . = 0 122 23 − 52 23 6 2∈9 N VK[S]b /
  20. 20. m m m m R W ?N W I J ?N W I J 5? I J y N VK[S]b m m O WKX =X] RW I J m v y r XM]U R (
  21. 21. l XM]U R w m k m m • h h m N VK[S]b ʼ m ( m k m • h l D(Q) “ x =X] RW ) ( ( ( , m ( m ( (
  22. 22. m m m m R W ?N W I J ?N W I J 5? I J y N VK[S]b m m O WKX =X] RW I J m v y r XM]U R o m WL N NW U 3PP NP RXW o( m =X] RW ( ((
  23. 23. l ­h w – AX N = – WL N NW U 3PP NP RXW I J AX N = m x ʼ m m h ʼ m x r x ()
  24. 24. l WL N NW U 3PP NP RXW – – AX N = WL N NW U 3PP NP RXW I J (
  25. 25. t l w h – m h ʻ h m ( ( m k ( k (+
  26. 26. AX N U t l r h – m m x m ʻ A 5 6 B p h 3 4w h 3v h 4v ) ( r h 4 sw w r A 5 6 ( ( m 1j2 h w (,
  27. 27. ­h l ­h – C]KXP [N O] [U 1XKVb S [ TOM] ” KL [K] [b P GOL 1VQ [S]RW + m l – SX a ( , . O[ O[ – 9X]OV HO X 3 E +, ( (-78c KXN 72 B1 – C]K]O P ]RO K[] 27 h3 Dataset |V| |E| Skewness of degree distribution dblp 326,186 1,615,400 2.82 live 5,363,260 79,023,142 2.29 uk-2005 39,459,925 936,364,282 1.71 webbase 118,142,155 1,019,903,190 2.14 uk-2007 105,896,555 3,738,733,648 1.51 (-
  28. 28. l 4 == - – [ ON SWS]ON ( – x x (f (. ) ( m m +,
  29. 29. l 4 == )f (/ MKU UR N ]T ) , NKK [N ]T ) . WL N NW U PP NP RXW / - /. /. /- 4 == .. - /- /, /- 5? .(
  30. 30. l BN[XU] RXW =R R H8XU ]W X ) /I – x ʼ – xh 7[ XN ][ ]R I J y ) . = 0 122 23 − ∑ 12AA∈9 23 6 2∈9 h ʼ x
  31. 31. )
  32. 32. l )( l y l y ü 9XM[OWOX]KV 1QQ[OQK]S X x ü (R K Kb X NO x ü 8 CRS UK K O] KV f6K ] 1VQ [S]RW P [ N VK[S]b LK ON 7[K R 3V ]O[SXQ g 9X [ M 1119 ( ) 8 CRS UK K O] KV fC31 0 5PPSMSOX] 1VQ [S]RW P [ 6SXNSXQ 3V ]O[ 8 L KXN ]VSO[ X K[QO MKVO 7[K R g F 42 ( +
  33. 33. y 0C53? IH J l r h c – m C][ M] [KV SWSVK[S]b m 9 7 8 6 3 4 0 5 2 1 10 11 12 13 mm ))
  34. 34. C ]L ] U [R RU R l h 6 3 0 2 1 4 5 “ h Γ S = {T ∶ S, T ∈ W} ∪ {S}Y S, T = |Γ S ∩ Γ(T)| Γ S |Γ(T)| y c m + 1 ʻʻ )
  35. 35. 1 y h h n h h 6 3 0 2 1 4 5 6 3 0 2 1 4 5 y h 6 3 0 2 1 4 5 h l y h h m LX N l h h m KX MN )+
  36. 36. LX N KX MN l LX N 0 h ] l y h h m LX Nl y h h m LX N ] x x ^ z m x ),
  37. 37. k = _. a, ] = I 6 3 0 5 2 1 4 -. 6 0 5 2 1 4 3 -. 6 0 2 1 4 3 5 )-
  38. 38. LX N KX MN l LX N 0 h ] l KX MN – M [O ^ m l y h h m LX Nl y h h m LX N ] x x ^ z m x l C53? c h , ] t v LX N KX MN z ).
  39. 39. C53? IH 44( -J r l 0 w r l j k x • ( m x • ^ h m C53? C53? w v r C53? X]WM ] r )/
  40. 40. C53? “ r C53? IH 44 ( -J h h CLX :RW 5U][ I2 []XO[ 9345 ( J PCTNUN XW5U] I8 KXQ D 45 ( )J m m =RWTC53? I SW 9345 ( J222 m ʼ ʻ
  41. 41. C53? C53? IH 44 ( -J h h CLX :RW 5U][ I2 []XO[ 9345 ( J PCTNUN XW5U] I8 KXQ D 45 ( )J m m =RWTC53? I SW 9345 ( J C53? ICRS UK K F 42 ( +J l C53? c v r – vC31
  42. 42. l ­ ( m m ) h h h M [O l ­ u h (
  43. 43. ­ l h ∃c ∈ de ∩ df ∧ c :h ijk1 ↔ de ∪ df ⊆ ne S T de df de ∩ df S T de ∪ df ne op ∩ oq LX N w ( m S, T m MKV MV ]O[ de, dfh C31 m S ne h i )
  44. 44. C53? l D X [N – ( m m Phase 1: Local clustering 9 7 8 6 3 0 5 2 1 4 10 11 12 Phase 2: Cluster refinement9 7 8 6 3 0 5 2 1 4 10 11 12 9 7 8 6 3 0 5 2 1 4 10 11 12 Local cluster D1B S ] MKV MV ]O[ MKV MV ]O[ m
  45. 45. A [N ( 0 =XL U LU][ N RWP l D3B r) h – m V MKV MV ]O[ ≥ _. a, ] ≥ I 6 3 0 5 2 1 4-. 6 3 0 5 2 1 4-. D1B P X NO 6 3 0 5 2 1 4-. MKV MV ]O[ P X NO l k( R K Kb [OKMRKLVO m X NO S (R Y S, c ≥ ^ X NO c m m S m T m c MKV MV ]O[ P X NOK RMPN +
  46. 46. A [N ) 0 5U][ N NORWN NW l r=XL U LU][ N h • MKV MV ]O[SXQ L[SNQO M [O – 2[SNQO M [O V MKV MV ]O[ m • L[SNQO M [O ][ M] [KV SWSVK[S]b ≥ _. a, ] ≥ I 6 3 0 5 2 1 4 MKV MV ]O[ MKV MV ]O[ ( X NO + M [O h MKV MV ]O[ ( 6 4 3 0 2 5 1 K RMPN ,
  47. 47. l CR RU R [ RWP – D1B l 3 L N R r – ] RK O MV ]O[SXQ K BON MO m m 6 3 0 5 2 1 4 7 ks(,, t) CR RU R [ RWP Γ 3 nΓ(0)m Y(3,4) = |v , ∩ v(t)| Γ 3 |Γ(4)| 6 3 0 5 2 1 4 7 -
  48. 48. C53? l – C31 D( 6@w 6xyw |W|) • i hz – ʼ l – C31 C31 • .
  49. 49. ( l – SX a ( , . O[ O[ – 9X]OV HO X 3 E +, ( (-78c – 72 B1 l ­h /
  50. 50. ) l • C53? – CSWSVK[S]b RK[SXQ h • C53? I J – • C53? I J – x C31 • PCTNUN XW5U] I J – x m ^ C31 +
  51. 51. (f l C53? C53? ) – x m x – QCUOVO] X3V C31 +
  52. 52. )f l C53? LX N 8 – C31 M [O x +(
  53. 53. *f l ­h – ( m h o , h 1 ( c h 1 - p +)
  54. 54. *f l h r – x m – x l( m caveman model) LKVKXMON ][OO +
  55. 55. l ++ l y l y ü 9XM[OWOX]KV 1QQ[OQK]S X x ü (R K Kb X NO x ü 8 CRS UK K O] KV f6K ] 1VQ [S]RW P [ N VK[S]b LK ON 7[K R 3V ]O[SXQ g 9X [ M 1119 ( ) 8 CRS UK K O] KV fC31 0 5PPSMSOX] 1VQ [S]RW P [ 6SXNSXQ 3V ]O[ 8 L KXN ]VSO[ X K[QO MKVO 7[K R g F 42 ( +
  56. 56. z j( )k l AE r – CSXQVO 7 E • I J j x j 7 E – V]S 7 E • I J KLOV [ KQK]S X KLOV [ KQK]S X 7 E l uz – I J I2KO KXN 2SVV C3d +J m m 7[K R KL x +, A 7D C 4 == ( 4 == ( 4 == Wi 4 ==
  57. 57. z j) )k l ]U R 5AE r – BKLLS] [NO[ I J 9XM[OWOX]KV 1QQ[OQK]S X I J 31C l 5 3 r – 8(. s , t +- 0 10 20 30 40 50 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Read[GB/s]
  58. 58. W NU GNXW A R – 9X]OV x m • 3 XSQR] 3 [XO[ XSQR] VKXNSXQ ( • -( • + ( C9 4 • x +. Knights Corner Knights landing
  59. 59. w +/ • SCAN • • Intel Xeon Phi 512 SIMD • Xeon Phi CPU / SIMD Xeon E5 1620 3.5 GHz 4/8 256 Xeon Phi 7250 1.4 GHz 68/272 512 webbase2001
  60. 60. fC53? X N GNXW A R , Xeon Phi SIMD , SCAN Xeon Phi
  61. 61. ­ , • core • • SIMD • • Union-Find • CAS • • • SCAN
  62. 62. ,( to 1 1 3 0 2 1 0 2 5 7 8 1 2 0 2 3 0 1 1 1 ptr to 0 0 1 1 1 2 2 3from CRS (Compressed Row Storage) 0 1 2 3 CRS • CRS • ptr from • Xeon Phi
  63. 63. h ­h ( ) l h h [X N PN SXRW c h l C 6 [RWPUN RW[ ]L RXW ]U R UN M ,) 3 4 10 13 20 … end 2 3 11 13 43 … end 3 3 4 4 2 3 2 3 Equals compare (4>3) 3 4 10 13 20 … end 2 3 11 13 43 … end advance pointer
  64. 64. , h ­h ) ) l ­h – ʼ h ʼ • • w v 3 4 10 13 20 … end 2 3 11 13 43 … end 3 3 3 3 2 3 11 13
  65. 65. l C53? LX Nv w w ,+ 6 3 4 5 0 2 1 Union-Find 2 10 3 5 4 6 Union-Find • Compare and Swap core core non-core
  66. 66. l C53? LX Nv w w ,, 6 3 4 5 0 2 1 Union-Find 6 3 4 5 0 2 1 2 10 3 5 4 6 Union-Find • Compare and Swap core core0 1,4,5 core non-core 2 1 0 3 54 6 Union-Find
  67. 67. l C53? LX Nv w w ,- 6 3 4 5 0 2 1 Union-Find 6 3 4 5 0 2 1 6 3 4 5 0 2 1 2 10 3 5 4 6 Union-Find • Compare and Swap core core0 1,4,5 5 2 ( ) core non-core 2 1 0 3 54 6 Union-Find 2 1 0 3 54 6 Union-Find CAS
  68. 68. ,. • • SCAN CPU • SCAN-XP CPU,KNC,KNL • - - 0 - 1,134,890 2,987,624 web-BerkStan 685,230 6,649,470 soc-Pokec 1,632,803 22,301,964 com-LiveJournal 3,997,962 34,681,189 soc-LiveJournal1 4,846,609 42,851,237 - 3,072,441 117,185,083 115,554,441 854,809,761 • • CPU Xeon E5 1620 (3.5 GHz, 4 , 8 ) Memory 16 GB • KNC Xeon Phi 3120A (1.10 GHz, 57 , 228 ) Memory 6GB • KNL Xeon Phi 7250 (1.4 GHz, 68 , 272 ) Memory 16GB (MCDRAM) + 96GB (DDR4)
  69. 69. ,/ 100 36 ! better N/A Executiontime(ms,logarithmic)
  70. 70. 5AE ?5 ?= - com-youtube 1 10 100 1000 10000 100000 Execution time (ms) com-LiveJournal 1 10 100 1000 10000 100000 Execution time (ms) com-Orkut 1 10 100 1000 10000 100000 Execution time (ms) soc-LiveJournal1 web-BerkStan 1 10 100 1000 10000 100000 Execution time (ms) 1 10 100 1000 10000 100000 Execution time (ms) 1 10 100 1000 10000 100000 Execution time (ms) soc-Pokecbetter better better better better better Executiontime(ms,logarithmic) Executiontime(ms,logarithmic) Executiontime(ms,logarithmic) Executiontime(ms,logarithmic) Executiontime(ms,logarithmic) Executiontime(ms,logarithmic) CPU KNC KNL SCAN-XPSCAN SCAN (Xeon,1) SCAN-XP(Xeon,1) SCAN-XP(Xeon,4) SCAN-XP(Xeon,8) SCAN-XP(KNC,57) SCAN-XP(KNC,114) SCAN-XP(KNC,171) SCAN-XP(KNC,228) SCAN-XP(KNL,68) SCAN-XP(KNL,136) SCAN-XP(KNL,204) SCAN-XP(KNL,272)
  71. 71. • m m – – BOKV [VN [ O[]b z ʻ - • m – HO X RS 7 E O]M • m – h h h h hp l – h l W N N[ RWP NW A XKUN [

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