Abstract
This paper studies linear layouts of generalized hypercubes, a d-dimensional c-ary clique and a d-dimensional c-ary array, and evaluates the bisection width, cut width, and total edge length of them, which are important parameters to measure the complexity of them in terms of a linear layout.
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References
L. N. Bhuyan and D. P. Agrawal. Generalized hypercube and hyperbus structures for a computer network. IEEE Transactions on Computers, C-33(4), April 1984.
G. Brebner. Relating routing and two-dimensinal grids. In P. Bertolazii and F. Luccio, editors, VLSI: Algorithms and Architectures, pages 221–231. Elsevier Science Publishers B.V.(North-Holland), 1985.
R. A. DeMillo, S. C. Eisenstat, and R. J. Lipton. Preserving average proximity in arrays. Communications of the ACM, 21(3):228–231, March 1978.
M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified polynomial complete problems. SIGACT, pages 47–63, 1974.
L. H. Harper. Optimal assignments of numbers to vertices. J. Soc. Indust. Appl. Math, 12(1):131–135, March 1964.
F. T. Leighton. Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks. MIT Press, 1983.
F. T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays · Trees · Hypercubes. Morgan Kaufmann, 1992.
F. Makedon and I. H. Subdorough. On minimizing width in linear layouts. Discrete Applied Mathematics, 23:243–265, 1989.
Y. Manabe, K. Hagihara, and N. Tokura. The minimum bisection widths of the cube-connected-cycles graph and cube graph. Trans. IEICE(D) Japan, J76-D(6):647–654, June 1984. in Japanese.
K. Nakano, W. Chen, T. Masuzawa, K. Hagihara, and N. Tokura. Cut width and bisection width of hypercube graph. IEICE Transactions, J73-A(4):856–862, April 1990. in Japanese.
L. Niepel and P. Tomasta. Elevation of a graph. Czechoslovak Mathematical Journal, 31(106):475–483, 1981.
A. L. Rosenberg. Preserving proximity in arrays. SIAM J. Comput., 4(4):443–460, December 1975.
C. D. Thompson. Area-time complexity for VLSI. In Proc. of 11th Symposium on Theory of Computing, pages 81–88. ACM, 1979.
K. Wada and K. Kawaguchi. Optimal bounds of the crossing number and the bisection width for generalized hypercube graphs. In Proc. of 16th Biennial Symposium on Communications, pages 323–326, May 1992.
K. Wada, H. Suzuki, and K. Kawaguchi. The crossing number of hypercube graphs. In Proc. of 43rd Convention of IPS Japan, pages 1–95, 1991. in Japanese.
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© 1994 Springer-Verlag Berlin Heidelberg
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Nakano, K. (1994). Linear layouts of generalized hypercubes. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_66
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DOI: https://doi.org/10.1007/3-540-57899-4_66
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-48385-4
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