KMcube: the compound of Kautz digraph and M?bius cube
KMcube: the compound of Kautz digraph and M?bius cube
Xianpeng HUANGFU, Deke GUO(), Honghui CHEN, Xueshan LUO
National Key Laboratory of Information System Engineering, School of Information System and Management, National University of Defense Technology, Changsha 410073, China
This paper introduces a novel interconnection network called KMcube (Kautz-M?bius cube). KMcube is a compound graph of a Kautz digraph and M?bius cubes. That is, it uses the M?bius cubes as the unit cluster and connects many such clusters by means of a Kautz digraph at the cost of only one additional arc being added to any node in each M?bius cubes. The topological benefits of both basic graphs are preserved in the compound network. It utilizes the topological properties of M?bius cubes to conveniently embed parallel algorithms into each cluster and the short diameter of a Kautz digraph to support efficient inter-cluster communication. Additionally, KMcube provides other attractive properties, such as the regularity, symmetry, and expandability. The proposed methodology for KMcube is further applied to the compound graphs of Kautz digraph and other M?bius-like graphs with the similar diameter to a M?bius cube.Moreover, other hybrid graphs of Kautz digraph and M?bius cubes are proposed and compared.
. KMcube: the compound of Kautz digraph and M?bius cube[J]. Frontiers of Computer Science, 2013, 7(2): 298-306.
Xianpeng HUANGFU, Deke GUO, Honghui CHEN, Xueshan LUO. KMcube: the compound of Kautz digraph and M?bius cube. Front Comput Sci, 2013, 7(2): 298-306.
Al-Fares M, Loukissas A, Vahdat A. A scalable, commodity data center network architecture. ACM SIGCOMM Computer Communication Review , 2008, 38(4): 63-74 doi: 10.1145/1402946.1402967
2
Guo C, Wu H, Tan K, Shi L, Zhang Y, Lu S. Dcell: a scalable and faulttolerant network structure for data centers. ACM SIGCOMM Computer Communication Review , 2008, 38(4): 75-86 doi: 10.1145/1402946.1402968
3
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 , 2009, 39(4): 63-74 doi: 10.1145/1594977.1592577
4
Guo D, Zhu G, Jin H, Yang P, Chen Y, Yi X, Liu J. M?bius-debruijn: The product of m?bius cube and debruijn digraph. Information Processing Letter , 2012, 112(5): 205-211 doi: 10.1016/j.ipl.2011.10.023
5
Wang C, Xiao L, Liu Y, Zheng P. Dicas: an efficient distributed caching mechanism for P2P systems. IEEE Transactions on Parallel and Distributed Systems , 2006, 17(10): 1097-1109 doi: 10.1109/TPDS.2006.137
6
Guo D, Wu J, Liu Y, Jin H, Chen H, Chen T. Quasi-kautz digraphs for peer-to-peer networks. IEEE Transactions on Parallel and Distributed Systems , 2011, 22(6): 1042-1055 doi: 10.1109/TPDS.2010.161
7
He Y, Liu Y. VOVO: vcr-oriented video-on-demand in large-scale peerto-peer networks. IEEE Transactions on Parallel and Distributed Systems , 2009, 20(4): 528-539 doi: 10.1109/TPDS.2008.102
8
Cull P, Larson S. Routing in twisted cube-like networks. In: Proceedings of the 2000 International Conference on Communications in Computing . 2000, 225
9
Agrawal D, Chen C, Burke J. Hybrid graph-based networks for multiprocessing. Telecommunication Systems , 1998, 10(1): 107-134 doi: 10.1023/A:1019158831409
10
Shen H, Xu C, Chen G. Cycloid: a constant-degree and lookupefficient P2P overlay network. Performance Evaluation , 2006, 63(3): 195-216 doi: 10.1016/j.peva.2005.01.004
11
Shen H, Xu C. Leveraging a compound graph-based dht for multiattribute range queries with performance analysis. IEEE Transactions on Computers , 2012, 61(4): 433-447 doi: 10.1109/TC.2011.30
12
Chen C, Agrawal D. dBCube: a new class of hierarchical multiprocessor interconnection networks with area efficient layout. IEEE Transactions on Parallel and Distributed Systems , 1993, 4(12): 1332-1344 doi: 10.1109/71.250115
13
Guo D, Chen H, He Y, Jin H, Chen C, Chen H, Shu Z, Huang G. KCube: a novel architecture for interconnection networks. Information Processing Letters , 2010, 110(18): 821-825 doi: 10.1016/j.ipl.2010.06.010
14
Larson S, Cull P. TheM?bius cubes. IEEE Transactions on Computers , 1995, 44(5): 647-659 doi: 10.1109/12.381950
15
Singhvi N, Ghose K. The Mcube: a symmetrical cube based network with twisted links. In: Proceedings of the 9th International Parallel Processing Symposium . 1995, 11-16 doi: 10.1109/IPPS.1995.395907
16
Guo D, Chen T, Li D, Liu Y, Liu X, Chen G. Bcn: expansible network structures for data centers using hierarchical compound graphs. In: Proceedings of the 2011 IEEE INFOCOM . 2011, 61-65 doi: 10.1109/INFCOM.2011.5935239
17
Panchapakesan G, Sengupta A. On a lightwave network topology using Kautz digraphs. IEEE Transactions on Computers , 1999, 48(10): 1131-1137 doi: 10.1109/12.805162
18
Miller M, ?irán J. Moore graphs and beyond: a survey of the degree/ diameter problem. Electronic Journal of Combinatorics , 2005, 61: 1-63
19
Ghozati S, Smires T. The fastcube: a variation on hypercube topology with lower diameter. Computers & Electrical Engineering , 2003, 29(1): 151-171 doi: 10.1016/S0045-7906(01)00021-0
20
Park J, Kim H, Lim H. Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements. IEEE Transactions on Parallel and Distributed Systems , 2006, 17(3): 227-240 doi: 10.1109/TPDS.2006.37
