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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
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•
• 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)
,/
100
36
!
better
N/A
Executiontime(ms,logarithmic)
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)
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Hiroaki Shiokawa

  • 1.
  • 2.
    Hiroaki Shiokawa h ­h Research Interests ­hc c ­h d DB w d 2011/4 2015/10 NTT 2015/11 (
  • 3.
  • 4.
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  • 14.
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  • 15.
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  • 18.
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  • 20.
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  • 23.
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  • 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.
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  • 30.
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  • 31.
  • 32.
    l )( l y l y ü9XM[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.
    y 0C53? IHJ 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.
    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.
    1 y hh 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.
    LX N KXMN l LX N 0 h ] l y h h m LX Nl y h h m LX N ] x x ^ z m x ),
  • 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.
    LX N KXMN 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.
    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.
    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.
    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.
    l ­ ( m m ) h h hM [O l ­ u h (
  • 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.
    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.
    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.
    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.
    l CR RUR [ 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.
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  • 49.
    ( l – SX a( , . O[ O[ – 9X]OV HO X 3 E +, ( (-78c – 72 B1 l ­h /
  • 50.
    ) l • C53? – CSWSVK[S]bRK[SXQ h • C53? I J – • C53? I J – x C31 • PCTNUN XW5U] I J – x m ^ C31 +
  • 51.
    (f l C53? C53?) – x m x – QCUOVO] X3V C31 +
  • 52.
    )f l C53? LXN 8 – C31 M [O x +(
  • 53.
    *f l ­h – (m h o , h 1 ( c h 1 - p +)
  • 54.
    *f l h r –x m – x l( m caveman model) LKVKXMON ][OO +
  • 55.
    l ++ l y l y ü9XM[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.
    z j( )k lAE 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.
    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.
    W NU GNXWA R – 9X]OV x m • 3 XSQR] 3 [XO[ XSQR] VKXNSXQ ( • -( • + ( C9 4 • x +. Knights Corner Knights landing
  • 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.
    fC53? X NGNXW A R , Xeon Phi SIMD , SCAN Xeon Phi
  • 61.
    ­ , • core • • SIMD • •Union-Find • CAS • • • SCAN
  • 62.
    ,( to 1 1 3 0 2 1 02 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.
    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.
    , 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.
    l C53? LXNv 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.
    l C53? LXNv 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.
    l C53? LXNv 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.
    ,. • • 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.
  • 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) CPUKNC 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.
    • 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 [