The exact gossiping problem for seven messages - Salvador, Karina Guada Ordoñez (2008)
This paper studies variation of the gossiping problem, where there are n persons, each one initially has a message. A pair can disseminate all messages they have by making one call. The exact gossiping problem is to determine the minimum number of calls each person to know exactly k messages. This is an extension of the papers by Tsay and Chang, Paredes and Paderanga, where the methods and techniques of Tsay and Chang were utilized for k=7. The study was able to obtain the minimum number of E(n,k) calls required for each person to know exactly k=7 messages, for all values of n7. In attaining the solution, graphs were provided by exhaustion to generate the possible component combinations of G, and made as basis for the general solution. To arrive at the solution, patterns from the results, were utilized and were then proven mathematically. To obtain solution for n7, n can be expressed as n=9m+r for some m0 and 7r15. To solve for the minimum number of E(n,7) calls the n vertices should be arranged into 9m components and the excess number of vertices that is r=n-9m, wherein r takes the values 7r15, which have E(n,k) values obtained from the graph.
Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2008
Keywords: Call sequences; Components; Gossiping; Gossiping -- Problems; Graphs