research-article

An efficient algorithm to construct disjoint path covers of DCell networks

Authors:

Cheng-Kuan LinAuthors Info & Claims

Theoretical Computer Science, Volume 609, Issue P1

Pages 197 - 210

https://doi.org/10.1016/j.tcs.2015.09.022

Published: 04 January 2016 Publication History

Abstract

Data center networks have been becoming more and more important with the development of cloud computing. For any two integers k 0 and n 2, the k-dimensional DCell with n-port switches, D k, n, has been proposed for one of the most important data center networks as a server centric data center network structure. D k, n can support millions of servers with outstanding network capacity and provide good fault tolerance by only using commodity switches. A disjoint path cover has significant applications in data center networks. In this paper, we prove that D k, n is one-to-one r-disjoint path coverable for any integer 1 r n + k - 1, except for D 1, 2 . Moreover, we propose an O ( t k ) algorithm for finding a one-to-one r-disjoint path cover in D k, n for any integer 1 r n + k - 1, where t k is the number of servers in D k, n .

References

[1]

X. Wang, J. Fan, B. Cheng, W. Liu, Y. Wang, One-to-one disjoint path covers in DCell, in: IFIP International Conference on Network and Parallel Computing, 2013, pp. 61-70.

Digital Library

[2]

S. Anthony, Microsoft now has one million servers. http://www.extremetech.com/extreme/161772-microsoft-now-has-one-million-servers-less-than-google-but-more-than-amazon-says-ballmer

[3]

S. Ghemawat, H. Gobioff, S. Leung, The Google file system, in: Symposium on Operating Systems Principles, 2003, pp. 29-43.

Digital Library

[4]

J. Dean, S. Ghemawat, MapReduce: simplified data processing on large clusters, Commun. ACM, 51 (2008) 107-113.

Digital Library

[5]

M. Isard, M. Budiu, Y. Yu, A. Birrell, D. Fetterly, Dryad: distributed data-parallel programs from sequential building blocks, in: European Conference on Computer Systems, 2007, pp. 59-72.

[6]

M. Al-fares, A. Loukissas, A. Vahdat, A scalable, commodity data center network architecture, in: Special Interest Group on Data Communication, 2008, pp. 63-74.

[7]

C. Guo, H. Wu, K. Tan, L. Shi, Y. Zhang, S. Lu, DCell: a scalable and fault-tolerant network structure for data centers, in: Special Interest Group on Data Communication, 2008, pp. 75-86.

[8]

C. Guo, G. Lu, D. Li, H. Wu, X. Zhang, Y. Shi, C. Tian, Y. Zhang, S. Lu, Bcube: a high performance, server-centric network architecture for modular data centers, in: Special Interest Group on Data Communication, 2009, pp. 63-74.

[9]

X. Yang, G.M. Megson, D.J. Evans, An oblivious shortest-path routing algorithm for fully connected cubic networks, J. Parallel Distrib. Comput., 66 (2006) 1294-1303.

Digital Library

[10]

D. Xiang, Y. Zhang, Y. Pan, Practical deadlock-free fault-tolerant routing in meshes based on the planar network fault model, IEEE Trans. Comput., 58 (2009) 620-633.

Digital Library

[11]

J. Fan, X. Jia, X. Liu, S. Zhang, J. Yu, Efficient unicast in bijective connection networks with the restricted faulty node set, Inform. Sci., 181 (2011) 2303-2315.

Digital Library

[12]

J. Fan, X. Jia, B. Cheng, J. Yu, An efficient fault-tolerant routing algorithm in bijective connection networks with restricted faulty edges, Theoret. Comput. Sci., 412 (2011) 3440-3450.

Digital Library

[13]

D. Xiang, Deadlock-free adaptive routing in meshes with fault-tolerance ability based on channel overlapping, IEEE Trans. Dependable Secure Comput., 8 (2011) 74-88.

Digital Library

[14]

K.-H. Kao, J.-M. Chang, Y.-L. Wang, J.S.-T. Juan, A quadratic algorithm for finding next-to-shortest paths in graphs, Algorithmica, 61 (2011) 402-418.

Digital Library

[15]

X. Yang, L. Wang, L. Yang, Optimal broadcasting for locally twisted cubes, Inform. Process. Lett., 112 (2012) 129-134.

Digital Library

[16]

D. Wang, Hamiltonian embedding in crossed cubes with failed links, IEEE Trans. Parallel Distrib. Syst., 23 (2012) 2117-2124.

Digital Library

[17]

D.-R. Duh, Y.-C. Lin, C.-N. Lai, Y.-L. Wang, Two spanning disjoint paths with required length in generalized hypercubes, Theoret. Comput. Sci., 506 (2013) 55-78.

Digital Library

[18]

B. Heller, S. Seetharaman, P. Mahadevan, Y. Yiakoumis, P. Sharma, S. Banerjee, N. McKeown, Elastictree: saving energy in data center networks, in: Symposium on Network System Design and Implementation, 2010, pp. 249-264.

[19]

C. Raiciu, S. Barre, C. Pluntke, A. Greenhalgh, D. Wischik, M. Handley, Improving datacenter performance and robustness with multipath TCP, in: Special Interest Group on Data Communication, 2011, pp. 266-277.

[20]

A. Deutsch, M. Fernandez, D. Suciu, Storing semistructured data with stored, SIGMOD Rec., 28 (1999) 431-442.

Digital Library

[21]

A.B. Kahng, J. Lach, W.H. Mangione-Smith, S. Mantik, I.L. Markov, M. Potkonjak, P. Tucker, H. Wang, G. Wolfe, Constraint-based watermarking techniques for design IP protection, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 20 (2001) 1236-1252.

Digital Library

[22]

R. Lin, S. Olariu, J.L. Schwing, J. Zhang, An efficient algorithm for minimum path cover and Hamiltonicity on cographs, Parallel Algorithms Appl., 2 (1994) 99-113.

[23]

A.S. Tanenbaum, Computer Networks, Prentice-Hall, Englewood Cliffs, NJ, 1981.

[24]

S.S. Pinter, Y. Wolfstahl, On mapping processes to processors in distributed systems, Int. J. Parallel Program., 16 (1987) 1-15.

Digital Library

[25]

Z. Zhou, S. Das, H. Gupta, Variable radii connected sensor cover in sensor networks, ACM Trans. Sens. Netw., 5 (2009) 1-36.

Digital Library

[26]

S.C. Ntafos, S.L. Hakimi, On structured digraphs and program testing, IEEE Trans. Comput., 30 (1981) 67-77.

Digital Library

[27]

J.-H. Park, H.-C. Kim, H.-S. Lim, Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements, IEEE Trans. Parallel Distrib. Syst., 17 (2006) 227-240.

Digital Library

[28]

M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979.

[29]

D.S. Johnson, The NP-completeness column: an ongoing guide, J. Algorithms, 3 (1982) 381-395.

[30]

L. You, J. Fan, Y. Han, X. Jia, One-to-one disjoint path covers on alternating group graphs, Theoret. Comput. Sci., 562 (2015) 146-164.

Digital Library

[31]

Y.-K. Shih, S.-S. Kao, One-to-one disjoint path covers on k-ary n-cubes, Theoret. Comput. Sci., 412 (2011) 4513-4530.

Digital Library

[32]

J. Li, D. Liu, Y. Yang, J. Yuan, One-to-one disjoint path covers on multi-dimensional tori, Int. J. Comput. Math., 92 (2015) 1-10.

Digital Library

[33]

J.-H. Park, One-to-one disjoint path covers in recursive circulants, J. KISS, 30 (2003) 691-698.

[34]

D. Li, C. Guo, H. Wu, K. Tan, Y. Zhang, S. Lu, Ficonn: using backup port for server interconnection in data centers, in: International Conference on Computer Communications, 2009, pp. 2276-2285.

[35]

H. Libdeh, P. Costa, A. Rowstron, G. O'Shea, A. Donnelly, Symbiotic routing in future data centers, in: Special Interest Group on Data Communication, 2010, pp. 51-62.

[36]

M. Manzano, K. Bilal, E. Calle, S.U. Khan, On the connectivity of data center networks, IEEE Commun. Lett., 17 (2013) 2172-2175.

[37]

M. Kliegl, J. Lee, J. Li, X. Zhang, C. Guo, D. Rincon, Generalized DCell structure for load-balanced data center networks, in: International Conference on Computer Communications, 2010, pp. 1-5.

[38]

X. Wang, A. Erickson, J. Fan, X. Jia, Hamiltonian properties of dcell networks, Comput. J. (2015).

[39]

D.B. West, Introduction to Graph Theory, vol. 2, Prentice, Upper Saddle River, 2001.

[40]

D. Abts, M.R. Marty, P.M. Wells, P. Klausler, H. Liu, Energy proportional datacenter networks, in: Special Interest Group on Data Communication, ACM, 2010, pp. 338-347.

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An efficient algorithm to construct disjoint path covers of DCell networks
1. Mathematics of computing
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cover image Theoretical Computer Science

Theoretical Computer Science Volume 609, Issue P1

January 2016

292 pages

ISSN:0304-3975

Issue’s Table of Contents

Copyright © Elsevier B.V.

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 04 January 2016

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Cited By

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An NLv MFan WHan LXiao F(2024)Extra connectivity of the data center network—RRectThe Journal of Supercomputing10.1007/s11227-024-06077-x80:11(16452-16473)Online publication date: 1-Jul-2024
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Zhang YFan WHan ZSong YWang R(2021)Fault-tolerant routing algorithm based on disjoint paths in 3-ary n-cube networks with structure faultsThe Journal of Supercomputing10.1007/s11227-021-03799-077:11(13090-13114)Online publication date: 1-Nov-2021
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