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Direct networks and asymmetric indirect networks -Advanced Networks-

Direct networks and asymmetric indirect networks -Advanced Networks-. AMANO, Hideharu Textbook pp.147 - 166. Basic direct networks. Linear. Central concentration. Ring. Tree. つりｘ. Complete connection. Mesh. Metrics of Direct interconnection network （ D and ｄ）. Diameter ： D

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Direct networks and asymmetric indirect networks -Advanced Networks-

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  1. Direct networks and asymmetric indirect networks-Advanced Networks- AMANO, Hideharu Textbook pp.147 - 166

  2. Basic direct networks Linear Central concentration Ring Tree つりｘ Complete connection Mesh

  3. Metrics of Direct interconnection network（D and ｄ） • Diameter：D • Number of hops between most distant two nodes through the minimal path • degree: d • The largest number of links per a node. • D represents performance and ｄ represents cost Recent trends: Performance: Throughput Cost: The number of long links

  4. Hypercube 0001 0000 0010 0011 0100 0111 0101 0110 1000 1001 1010 1011 1100 1101 1110 1111

  5. ｋ-ａｒｙ　ｎ-ｃｕｂｅ • Generalized mesh/torus • K-ary n digits number is assigned into each node • For each dimension (digit), links are provided to nodes whose number are the same except the dimension in order. • Rap-around links (ｎ-1→０) form a torus, otherwise mesh.

  6. ０ ０ ０ ２ ２ ２ ０ ０ １ １ １ ０ 3-ary1-cube １ １ １ 3-ary2-cube ２ ２ ２ k-aryn-cube

  7. ２ ２ ２ １ １ １ ０ ０ ０ ２ ２ ２ ０ ０ ０ ０ ０ ０ ０ ０ １ １ １ ０ ０ ０ ０ ２ １ １ １ ０ １ １ １ ０ ０ ０ ０ １ １ １ ０ １ １ １ ２ ２ ２ １ １ １ １ ２ ２ １ １ １ 3-ａｒｙ　3-ｃｕｂｅ ０ ２ ２ ２ ０ ０ ０ ０ ２ ２ ２ ０ ２ ２ ２ ２ ２ ２ １ １ １ k-aryn-cube 3-ary1-cube 3-ary2-cube

  8. 1*** 2*** ３-ary4-cube 0***

  9. Interconnection networks for a large scale parallel machines or clusters • Hypercubes → 2D/3D mesh/torus • small d, easy to implement • killer applications like partial differential equations and image processing. • locality of communication • However, if the number of nodes is large, too large diameter Large scale interconnection networks

  10. Advanced direct networks • Shuffle based networks • DeBruijn, Kautz, Pradhan • Extended mesh/torus • Midimew, RDT • StarGraph • Hierarchical networks • CCC, Hypernet • Circular networks • CircularOmega、MDCE

  11. De Bruijn network 001 011 000 010 101 111 110 100 0 1

  12. Routings for De Bruijn 001 011 000 010 101 111 110 100 0 DestinationRouting (001→101) 1

  13. 0 1 k-1 .. .. .. .. B(k，n) K-ary n-digits

  14. Characteristics of De Bruijn • Benefits • d=2k、D=n=logN • When k=2, d=4、D=logＮ，that is, d of 2-dimensional mesh but D of hypercube. • Problems • Optimal routing is difficult (not established yet). • Destinationrouting cannot make a best use of communication locality. • No killer applications. • Self loop and duplicated links

  15. Other shuffle based networks • Kautz • No self loops • Pradhan • Fault tolerant • Similar weak points of DeBruijn network • Irregular node numbers

  16. Kautz network 210 The same number should not be at the neighboring digit 121 101 012 010 212 120 201 102 021 202 020

  17. Pradhan network 1bit left rotation: shuffle + Additional link 100 101 001 110 111 000 011 010

  18. Circular networks • CircularOmega • Advantageous for one-way communication • Used in data-flow machine EM-4 • MDCE(CCCB) • Hierarchical structure of CircularOmega（Banyan） • Used in massively parallel machine RWC-1

  19. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 CircularOmega network

  20. Cube Connected Circular Banyan Circular Banyan 3-Dimensional Proposed for RWC-1

  21. Star graph ABCD DBCA CBAD CBDA BACD BDCA BACD CABD CDBA BCDA ACBD DCBA CDAB BDAC ADCB DBAC DCAB ADBC ACDB DACB DABC ABDC CADB BADC Connection n! nodes

  22. Routing on Star graph ABCD DBCA CBAD CBDA BACD BDCA BACD CABD CDBA BCDA ACBD DCBA CDAB BDAC ADCB DBAC DCAB ADBC ACDB DACB DABC ABDC CADB BADC If Ａ is top, change with arbitrary symbol, else, change with the symbol of destination node ＡＢＣＤ　→　ＤＡＢＣ ３（ｎ－１）／２

  23. Hierarchical network • CCC(CubeConnectedCycles) • ｈｙｐｅｒｃｕｂｅ＋loop • Hypernet • Compete connection＋hypercube • Well combined, weak points of original networks are vanished. • Complicated routing, gap between hierarchies

  24. CCC(CubeConnectedCycles) 000 001 100 101 0 1 2 011 010 110 111

  25. Hyper Net h i d b o a c b j c e d k h f m e f g l a n g p Other links are used for further upper hierarchy

  26. Extended mesh/torus • Including mesh/torus structure • Extended links for performance enhancement • ReconfigurableMesh • Midimew • RDT

  27. RDT(RecursiveDiagonalTorus)

  28. Multicasting on the RDT

  29. Asymmetric indirect networks • Using switching boxes for connecting nodes • Single link per node type →Suitable for PC clusters • Intermediate position between direct and indirect networks • High communication capability considering cost • base-mn-cube（Hyper crossbar） • SR2000、CP-PACS • Hyper-cross • ADENART • FatTree • CM-5，Autonet, QsNet • Myrinet Clos • Myrinet

  30. base-mn-cube(Hyper crossbar) crossbar router PU Used in Toshiba’s Prodigy and Hitachi’s SR8000

  31. HyperCross (pi,pj)→ (pj,*),(*,pi) (2,1) → (1,*),(*,2) 0,0 0,3 Xbar (1,*) 2,1 3,0 3,3 Used in ADENART by Matsushita

  32. HyperCross (pi,pj)→ (pj,*),(*,pi) (2,1) → (1,*),(*,2) 0,0 0,3 Xbar (*,2) 2,1 3,0 3,3 Skewed Interconnection Destination routing is possible like De Bruijn Network

  33. FatTree Used in CM-5 and PCClusters( QsNet, Autonet )

  34. FatTree MIN like style

  35. FatTree Myrinet-Clos

  36. Summary • Recently, practical new topologies are not proposed. • A lot of “made-in-Japan” networks • Asymmetric indirect networks will be widely used.

  37. Exercise • Calculate Diameter (D) of Cube Connected Cycle with 16 rings (cycles) each of which has four nodes (That is, a system with 64 nodes).

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