Abstract
A graph G = (V, E) is called a hyper-ring with N nodes (N-HR for short) if V = {0,..., N - 1} and E = {{u,v}|v - u modulo N is a power of 2}. The following results are shown. We prove that the node-connectivity κ of an N-HR is equal to its degree, say δ, by presenting an algorithm for the explicit construction of δ node-disjoint paths connecting nodes s and t. The length of these paths is bounded by [logD]+3, where D is the positional distance between s and t. Finally, we show a node-to-node communication scheme for HRs that requires only [log D]+3 rounds, even in the presence of up to δ - 1 node failures.
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References
N. Alon, A. Barak, and U. Mauber, On disseminating information reliably without broadcasting, 7th Int. Conference on Distributed Computer Systems (1987) 74–81.
T. Altman, Y. Igarashi, and K. Obokata, Hyper-ring connection machines, Parallel Computing 21 (1995) 1327–1338.
T. Altman, Reliable communication schemes for hyper-rings, 28th Int. Southeastern Conference on Combinatorics, Graph Theory, and Computing (1997).
F. Boesch and A. Felzer, A general class of invulnerable graphs, Networks 2 (1972) 261–283.
F. Boesch and R. Tindell, Circulants and their connectivities, J. of Graph Theory 8 (1984) 487–499.
E. van Doorn, Connectivity of circulant digraphs, J. of Graph Theory 10 (1986) 9–14.
Y. Han, R. Finkel, An optimal scheme for disseminating information, The 22nd Int. Conference on Parallel Processing (1988) 198–203.
Y. Han, Y. Igarashi, K. Kanai, and K. Miura, Broadcasting in faulty binary jumping networks, J. of Parallel and Distributed Computing 23 (1994) 462–467.
W. Knödel, New gossips and telephones, Discrete Mathematics 13 (1975) 95.
A. Pelc, Fault-tolerant broadcasting and gossiping in communication networks, Networks 28 (1996) 143–156.
M. O. Rabin, Efficient dispersal of information for security, load balancing, and fault tolerance, J. of ACM 36 (1989) 335–348.
D. West, Introduction to Graph Theory, Prentice Hall (1996).
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© 2002 Springer-Verlag Berlin Heidelberg
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Altman, T., Igarashi, Y., Motegi, K. (2002). Fast and Dependable Communication in Hyper-rings. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_38
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DOI: https://doi.org/10.1007/3-540-45655-4_38
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