Browse > Article

Embedding Multiple Meshes into a Twisted Cube  

Kim, Sook-Yeon (한경대학교 컴퓨터공학과)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.37, no.2, 2010 , pp. 61-65 More about this Journal
Abstract
The twisted cube has received great attention because it has several superior properties to the hypercube that is widely known as a versatile parallel processing system. In this paper, we show that node-disjoint $2^{n-1}$ meshes of size $2^n{\times}2^m$ can be embedded into a twisted cube with dilation 1 where $1{\leq}n{\leq}m$. The expansion is 1 for even m and 2 for odd m.
Keywords
twisted cube; mesh; embedding; dilation; expansion;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C.-J. Lai, C.-H. Tsai, "Embedding a family of meshes into twisted cubes," Information Processing Letters, vol.108, Issue 5, pp.326-330, Nov. 2008.   DOI   ScienceOn
2 B. Monien, H. Sudborough, "Embedding one interconnection network in another," pp.257-282, Springer-Verlag/Wien, 1990. Computing Supplementum 7: Computational Graph Theory.
3 A. Rosenberg, "Issues in the study of graph embeddings," Lecture Notes in Computer Science, Springer-Verlag, New York, vol.100, pp.150-176, 1981.
4 F. Berman, L. Snyder, "On mapping parallel algorithms into parallel architectures," J. Parallel Distrib. Comput., vol.4, no.5, pp.439-458, 1987.   DOI   ScienceOn
5 V. Chaudhary, J.K. Aggarwal, "Generalized mapping of parallel algorithms onto parallel architectures," Proc. Int'l Conf. Parallel Processing, pp. 137-141, Aug. 1990.
6 S. L. Bezrukov, J. D. Chavez, L. H. Harper M. Rottger, U.-P. Schroeder, "The congestion of n-cube layout on a rectangular grid," Discrete Math., vol.213, no.1-3, pp.13-19, Feb. 2000.   DOI   ScienceOn
7 J. Fan, X. Lin, "The t/k-diagnosability of the BC Graphs," IEEE Trans. Computers, vol.54, no.2, pp.176-184, 2005.   DOI   ScienceOn
8 M.-C. Yang, T.-K. Li, J. J. M. Tan, L.-H. Hsu, "On embedding cycles into faulty twisted cubes," Information Sciences, vol.176, no.6, pp.676-690, 2006.   DOI   ScienceOn
9 J.-S. Fu, "Fault-free Hamiltonian cycles in twisted cubes with conditional link faults," Theoretical Computer Science, vol.407, no.1-3, pp.318-329, Nov. 2008.   DOI   ScienceOn
10 J. Fan, X. Lin, Y. Pan, X. Jia, "Optimal faulttolerant embedding of paths in twisted cubes," J. Parallel Distrib. Comput., vol.67, no.2, pp.205-214, 2007.   DOI   ScienceOn
11 S.-Y. Kim, "Embedding a mesh of size $2^{n}$${\times}$$2^{m}$ into a twisted cube," The Transactions of the Korea Information Processing Society A, vol.16-A, no.4, pp.223-226, 2009.   과학기술학회마을   DOI   ScienceOn
12 P. A. J. Hilbers, M. R. J. Koopman, J. L. A. van de Snepscheut, "The twisted cube," in PARLE: Parallel Architectures and Languages Europe, Parallel Architectures, vol.1, Springer, Berlin, pp.152- 158, 1987.
13 S. Abraham, K. Padmanabhan, "The twisted cube topology for multiprocessors: a study in network asymmetry," J. Parallel Distrib. Comput., vol.13, Issue 1, pp.104-110, 1991.   DOI   ScienceOn
14 C.-P. Chang, J.-N. Wang, L.-H. Hsu, "Topological properties of twisted cube," Information Sciences, vol.113, pp.147-167, 1999.   DOI   ScienceOn
15 E. Abuelrub, S. Bettayeb, "Embedding complete binary trees into twisted hypercubes," Proc. of the Int. Conf. on Computer Applications in Design, Simulation and Analysis, Washington, D.C. March 10-12, pp.1-4, 1992.
16 A. Patel, A. Kusalik, C. McCrosky, "Area-efficient VLSI layouts for binary hypercubes," IEEE Trans. Computers, vol.49, no.2, pp.160-169, Feb. 2000.   DOI   ScienceOn
17 J. Fan, X. Lin, X. Jia, R. W. H. Lau, "Edgepancyclicity of twisted cubes," ISAAC 2005, Lecture Notes in Comput. Sci., vol.3827, pp.1090- 1099, 2005.
18 W.-T. Huang, J. J. M. Tan, C.-N. Hung, L.-H. Hsu, "Fault-tolerant hamiltonicity of twisted cubes," J. Parallel Distrib. Comput., vol.62, no.4, pp.591-604, 2002.   DOI   ScienceOn
19 A. Matsubayashi, "VLSI layout of trees into grids of minimum width," IEICE Trans. Fundamentals, vol.E87-A, no.5, pp.1059-1069, May 2004.
20 Q. Dong, X. Yang, J. Zhao and Y. Y. Tang, "Embedding a family of disjoint 3D meshes into a crossed cube," Information Sciences, vol.178, Issue 11, pp.2396-2405, June 2008.   DOI   ScienceOn