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Some New Directions about Interconnection Networks

Some New Directions about Interconnection Networks. Purpose of this talk. A story of research How to do research as a student How to do research as a professor. Interconnection Networks. Hypercubes. 100. 110. 0. 00. 10. 000. 010. 101. 111. 1. 01. 11. 001. 011. Q 1. Q 2. Q 3.

melodie-owens
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Some New Directions about Interconnection Networks

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  1. Some New Directions about Interconnection Networks

  2. Purpose of this talk • A story of research • How to do research as a student • How to do research as a professor

  3. Interconnection Networks

  4. Hypercubes 100 110 0 00 10 000 010 101 111 1 01 11 001 011 Q1 Q2 Q3

  5. Let u = un−1un−2. . .u1u0 and v = vn−1vn−2. . .v1v0 be two n-bit binary strings. • The Hamming distanceh(u, v) between two vertices u and v is the number of different bits in the corresponding strings of both vertices. • The n-dimensional hypercubeconsists of all n-bit binary strings as its vertices and two vertices u and v are adjacent if and only if h(u, v) = 1.

  6. Hypercubic Like graphs • Twisted cubes • Cross cubes • Mobius cubes • Locally twisted cubes n regular graph with 2n vertices

  7. Bypartite Hypercubic Like Graphs

  8. Other Cubic Graphs • Folded hypercubes (bipartite or nonbipartite) • Enhance hypercubes (bipartite or nonbipartite) • Augmented cubes

  9. Other Families • Star graphs (bipartite) • Pancake graphs • (n,k)-star graphs • Arrangement graphs • Butterfly (bipartite or nonbipartite) • Recursive circulant graphs • Cubic family (honeycomb torus, Christmas tree, honeycomb disk, spider web, brother tree) • etc

  10. S. Latifi, S. Zheng, N. Bagherzadeh, Optimal ring embedding in hypercubes with faulty links, in: Fault-Tolerant Computing Symp., 1992, pp. 178–184. • Y.C. Tseng, S.H. Chang, and J.P. Sheu, Fault-tolerant ring embedding in a star graph with both link and node failures, IEEE Trans Parallel Distrib Syst 8 (1997), 1185–1195.

  11. Another story • F. Harary, J.P. Hayes, Edge fault tolerance in graphs, Networks 23 (1993) 135–142. • F. Harary, J.P. Hayes, Node fault tolerance in graphs, Networks 27 (1996) 19–23. Diameter about n/4

  12. K.Mukhopadhyaya, B.P. Sinha, Hamiltonian graphs with minimum number of edges for fault-tolerant topologies, Inform. Process. Lett. 44 (1992) 95–99. Diameter about n/6

  13. Diameter about O(n1/2) Diameter about O(log n)

  14. Fault Hamiltonian and Fault Hamiltonian Connected

  15. Home Home Home

  16. Fault Hamiltonian and Fault Hamiltonian Connected • n-2 fault tolerant hamiltonian and n-3 fault tolerant hamiltonian connected • d-2 fault tolerant hamiltonian and d-3 fault tolerant hamiltonian connected

  17. General Rules • Y. C. Chen, C. H. Tsai, L. H. Hsu, and Jimmy J. M. Tan (2004), "On some super fault-tolerant Hamiltonian graphs," Applied Mathematics and Computation, Vol. 148, pp. 729-741.

  18. Other families of Interconnection Networks • C.H. Tsai, J.M. Tan, Y.C. Chen, and L.H. Hsu, (2002) "Hamiltonian Properties of Faulty Recursive Circulant Graphs," Journal of Interconnection Networks, Vol 3, Nos, 3&4, pp. 273-289. • C.N. Hung, H. C. Hsu, K. Y. Liang, and L. H. Hsu, (2003) "Ring Embedding in Faulty Pancake Graphs," Information Processing Letters, Vol 86, pp. 271-275.

  19. H.C. Hsu, Y.L. Hsieh, J.M. Tan, and L.H. Hsu, (2003) " Fault Hamiltonicity and Fault Hamiltonian Connectivity of the (n,k)-star Graphs," Networks, Vol 42(4), pp. 189-201. • H.C. Hsu, T.K. Li, J.M. Tan, and L.H. Hsu (2004). "Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs," IEEE Trans. on Computers, Vol. 53 (1), pp. 39-53.

  20. C.H. Tsai, J.M. Tan, T. Liang, and L.H. Hsu (2002), ``Fault-Tolerant Hamiltonian Laceability of Hypercubes", Information Processing Letters, Vol. 83, pp. 301-306. • H.C. Hsu, L.C.Chiang, Jimmy J.M. Tan, L.H. Hsu (2005), `` Fault hamiltonicity of augmented cubes", Parallel Computing, Vol. 31, pp.131-145. • Y.H. Teng, Jimmy J.M. Tan, L.H. Hsu (2005), ``Honeycomb rectangular disks", Parallel Computing, Vol. 31, pp.371-388.

  21. How about bipartite graphs Hamiltonian laceable

  22. Edge fault tolerance hamiltonian laceable

  23. Edge fault tolerance strong hamiltonian laceable

  24. Hyper hamiltonian laceable

  25. pancyclic

  26. pancyclic

  27. Panconnected • A lot of people work on pancyclic and panconnected recently.

  28. Globally 3*-connected Graphs • M. Albert, E.R.L. Aldred, D. Holton, and J. Sheehan, On globally 3*-connected graphs, Australasian Journal of Combinatorics, 24, 2001, 193-207.

  29. Global 3*-connected graph

  30. Mutually independent hamiltonian cycles and hamiltonian paths

  31. 出入口

  32. 出入口

  33. Mutually independent hamiltonian cycles and hamiltonian paths

  34. Star and cycle (independent hamiltonian cycles) • (n,k)-star graph (independent hamiltonian paths) • Folded hypercubes (KBJ) • Other families of graphs and math works • Independent paths and cycles

  35. 0 出入口 1 1 2 2 2 2 3 2 1 2 1 Panpositionable Hamiltonian

  36. 出入口 出入口

  37. Panpositionable Hamiltonian

  38. Diagnosability

  39. Thanks

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