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Neighborhood Information Dissemination in the Star Graph
December 2000 (vol. 49 no. 12)
pp. 1366-1370

Abstract—This paper studies two neighborhood information dissemination problems in the star graph (n-star): The neighborhood broadcast problem (NBP) is the problem of disseminating a message from the source vertex to all the vertices adjacent to the source vertex and the neighborhood gossiping problem (NGP) is the problem of exchanging messages among all neighboring vertices in the given graph. We propose two neighborhood information dissemination schemes in n-star under the single-port, half-duplex model: The first scheme completes a neighborhood broadcast in $1.5\log_2 n + O(1)$ time units and the second scheme completes a neighborhood gossiping in $2.88\log_2 n + o(\log n)$ time units. We also derive a lower bound on the neighborhood gossiping of $2.88\log_2 n + O(1)$ time units, which implies that the latter scheme is optimal with respect to the leading term.

[1] S.B. Akers and B. Krishnamurthy, “A Group-Theoretic Model for Symmetric Interconnection Networks,” IEEE Trans. Computers, vol. 38, no. 4, pp. 555-566, Apr. 1989.
[2] S.G. Akl and K. Qiu, “Fundamental Algorithms for the Star and Pancake Interconnection Networks with Applications to Computational Geometry,” Networks, vol. 23, pp. 215-225, 1993.
[3] S.G. Akl and K. Qiu, “A Novel Routing Scheme on the Star and Pancake Networks and Its Applications,” Parallel Computing, vol. 19, pp. 95-101, 1993.
[4] N. Bagherzadeh, N. Nassif, and S. Latifi, “A Routing and Broadcasting Scheme on Faulty Star Graphs,” IEEE Trans. Computers, vol. 42, no. 11, pp. 1,398-1,403, Nov. 1993.
[5] P. Berthome, A. Ferreira, and S. Perennes, “Optimal Information Dissemination in Star and Pancake Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 12, pp. 1,292-1,300, Dec. 1996.
[6] R.C. Entringer and P.J. Slater, “Gossips and Telegraphs,” J. Franklin Inst., vol. 307, pp. 353-360, 1979.
[7] S. Even and B. Monien, “On the Number of Rounds Necessary to Disseminate Information,” Proc. First ACM Symp. Parallel Algorithms and Architectures, pp. 318-327, 1989.
[8] P. Fragopoulou and S.G. Akl, “Optimal Communication Algorithms on Star Graphs Using Spanning Tree Constructions,” J. Parallel and Distributed Computing, vol. 24, pp. 55-71, 1995.
[9] P. Fragopoulou and S.G. Akl, “Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance,” IEEE Trans. Computers, vol. 45, no. 2, pp. 174-185, Feb. 1996.
[10] P. Fraigniaud and E. Lazard, “Methods and Problems of Communication in Usual Networks,” Technical Report 91-33, LIP ENS-Lyon, 1991.
[11] S. Fujita, S. Perennes, and J. Peters, “Neighbourhood Gossiping in Hypercubes,” Parallel Processing Letters, vol. 8, no. 2, pp. 189-195, 1998.
[12] S.W. Graham and S.R. Seidel, "The Cost of Broadcasting on Star Graphs and K-ary Hypercubes," IEEE Trans. Computers, vol. 42, no. 6, pp. 756-759, June 1993.
[13] S.M. Hedetniemi, S.T. Hedetniemi, and A.L. Liestman, “A Survey of Gossiping and Broadcasting in Communication Networks,” Networks, vol. 18, pp. 319-349, 1988.
[14] J. Hromkovic, R. Klasing, B. Monien, and R. Peine, “Dissemination of Information in Interconnection Networks (Broadcasting and Gossiping).” Combinatorial Network Theory, F. Hsu and D.-Z. Du, eds., Science Press&AMS, 1995.
[15] D.W. Krumme, “Fast Gossiping for the Hypercube,” SIAM J. Computing, vol. 21, no. 2, pp. 365-380, Apr. 1992.
[16] D.W. Krumme, G. Cybenko, and K.N. Venkataraman, “Gossiping in Minimal Time,” SIAM J. Computing, vol. 21, no. 1, pp. 111-139, Feb. 1992.
[17] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[18] V.E. Mendia and D. Sarkar, “Optimal Broadcasting in the Star Graph,” IEEE Trans. Parallel and Distributed Systems, vol. 3, pp. 389-396, July 1992.
[19] J.-P. Sheu, C.-T. Liaw, and T.-S. Chen, “A Broadcasting Algorithm in Star Graph Interconnection Networks,” Information Processing Letters, vol. 48, pp. 237-241, 1993.
[20] J.-P. Sheu, C.-T. Liaw, and T.-S. Chen, “An Optimal Broadcasting Algorithm without Message Redundancy in Star Graphs,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 6, June 1995.

Index Terms:
Interconnection network, information dissemination, broadcast, gossip, star graph.
Satoshi Fujita, "Neighborhood Information Dissemination in the Star Graph," IEEE Transactions on Computers, vol. 49, no. 12, pp. 1366-1370, Dec. 2000, doi:10.1109/12.895865
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