论文信息 - Quick Gossiping Without Duplicate Transmissions

Quick Gossiping Without Duplicate Transmissions

In this paper we are interested in the combination of Problems (A) and (B). Let f ( n ) denote the minimal number of calls in calling schemes among n persons where everybody hears each gossip exactly once. West [l5] showed that f ( n ) I 2.251 6, if n = 4k, k 2 2. Based on his ideas, we prove f ( n ) I 2.25n 3.5, if n = 4k + 2, k 2 5. On the other hand, West [14] provedf(n) 2 2n 3, if n > 8. The main result of this paper is as follows.

Ákos Seress

[1] Daniel J. Kleitman,et al. Further gossip problems , 1980, Discret. Math..

[2] Brenda S. Baker,et al. Gossips and telephones , 1972, Discret. Math..

[3] Ákos Seress. Gossiping old ladies , 1983, Discret. Math..

[4] Frank Harary,et al. The communication problem on graphs and digraphs , 1974 .

[5] Douglas B. West. A class of solutions to the gossip problem, part I , 1982, Discret. Math..

[6] D. West. GOSSIPING WITHOUT DUPLICATE TRANSMISSIONS , 1982 .

[7] E. C. Milner,et al. A Cure for the Telephone Disease , 1972, Canadian Mathematical Bulletin.

[8] Ákos Seress. Quick gossiping without duplicate transmissions , 1986, Graphs Comb..

[9] Douglas B. West. A class of solutions to the gossip problem, part II , 1982, Discret. Math..

[10] Ákos Seress. Quick Gossiping by Conference Calls , 1988, SIAM J. Discret. Math..

[11] Kenneth Lebensold. Efficient Communication by Phone Calls , 1973 .

[12] R. Bumby. A Problem with Telephones , 1981 .