Abstract
DCell has been proposed for one of the most important data center networks as a server centric data center network structure. DCell can support millions of servers with outstanding network capacity and provide good fault tolerance by only using commodity switches. In this paper, we prove that there exist r vertex disjoint paths {P i | 1 ≤ i ≤ r} between any two distinct vertices u and v of DCell k (k ≥ 0) where r = n + k − 1 and n is the vertex number of DCell 0. The result is optimal because of any vertex in DCell k has r neighbors with r = n + k − 1.
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Ghemawat, S., Gobioff, H., Leung, S.: The Google file system. ACM SIGOPS Operating Systems Review 37(5), 29–43 (2003)
Dean, J., Ghemawat, S.: MapReduce: Simplified data processing on large clusters. Communications of the ACM 51(1), 107–113 (2008)
Isard, M., Budiu, M., Yu, Y., Birrell, A., Fetterly, D.: Dryad: distributed data-parallel programs from sequential building blocks. ACM SIGOPS Operating Systems Review 41(3), 59–72 (2007)
Guo, C., Wu, H., Tan, K., Shi, L., Zhang, Y., Lu, S.: Dcell: a scalable and fault-tolerant network structure for data centers. ACM SIGCOMM Computer Communication Review 38(4), 75–86 (2008)
Guo, C., Lu, G., Li, D., Wu, H., Zhang, X., Shi, Y., Tian, C., Zhang, Y., Lu, S.: BCube: a high performance, server-centric network architecture for modular data centers. ACM SIGCOMM Computer Communication Review 39(4), 63–74 (2009)
Li, D., Guo, C., Wu, H., Tan, K., Zhang, Y., Lu, S.: FiConn: Using backup port for server interconnection in data centers. In: IEEE INFOCOM, pp. 2276–2285 (2009)
Li, D., Guo, C., Wu, H., Tan, K., Zhang, Y., Lu, S., Wu, J.: Scalable and cost-effective interconnection of data-center servers using dual server ports. IEEE/ACM Transactions on Networking 19(1), 102–114 (2011)
Lin, X., Philip, P., Ni, L.: Deadlock-free multicast wormhole routing in 2-D mesh multicomputers. IEEE Transactions on Parallel and Distributed Systems 5(8), 793–804 (1994)
Wang, N., Yen, C., Chu, C.: Multicast communication in wormhole-routed symmetric networks with hamiltonian cycle model. Journal of Systems Architecture 51(3), 165–183 (2005)
Lin, C., Huang, H., Hsu, L.: On the spanning connectivity of graphs. Discrete Mathematics 307(2), 285–289 (2007)
Lin, C., Huang, H., Tan, J., Hsu, L.: On spanning connected graphs. Discrete Mathematics 308(7), 1330–1333 (2008)
West, D.B., et al.: Introduction to graph theory, p. 2. Prentice Hall, Englewood Cliffs (2001)
Park, J., Kim, C., Lim, S.: Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements. IEEE Transactions on Parallel and Distributed Systems 17(3), 227–240 (2006)
Caha, R., Koubek, V.: Spanning multi-paths in hypercubes. Discrete Mathematics 307(16), 2053–2066 (2007)
Chen, X.: Many-to-many disjoint paths in faulty hypercubes. Information Sciences 179(18), 3110–3115 (2009)
Chen, X.: Paired many-to-many disjoint path covers of hypercubes with faulty edges. Information Processing Letters 112(3), 61–66 (2012)
Park, J., Kim, H., Lim, H.: Many-to-many disjoint path covers in the presence of faulty elements. IEEE Transactions on Computers 58(4), 528–540 (2009)
Ma, M.: The spanning connectivity of folded hypercubes. Information Sciences 180(17), 3373–3379 (2010)
Shih, Y., Kao, S.: One-to-one disjoint path covers on k-ary n-cubes. Theoretical Computer Science 412(35), 4513–4530 (2011)
Hsu, H., Lin, C., Hung, H., Hsu, L.: The spanning connectivity of the (n, k)-star graphs. International Journal of Foundations of Computer Science 17(2), 415–434 (2006)
Chen, X.: Unpaired many-to-many vertex-disjoint path covers of a class of bipartite graphs. Information Processing Letters 110(6), 203–205 (2010)
Huanga, P., Hsub, L.: The spanning connectivity of line graphs. Applied Mathematics Letters 24(9), 1614–1617 (2011)
Kliegl, M., Lee, J., Li, J., Zhang, X., Guo, C., Rincon, D.: Generalized DCell structure for load-balanced data center networks. In: IEEE INFOCOM Conference on Computer Communications Workshops, pp. 1–5 (2010)
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Wang, X., Fan, J., Cheng, B., Liu, W., Wang, Y. (2013). One-to-One Disjoint Path Covers in DCell. In: Hsu, CH., Li, X., Shi, X., Zheng, R. (eds) Network and Parallel Computing. NPC 2013. Lecture Notes in Computer Science, vol 8147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40820-5_6
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DOI: https://doi.org/10.1007/978-3-642-40820-5_6
Publisher Name: Springer, Berlin, Heidelberg
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