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Gossiping

Gossiping . Tam Phuong Nguyen Wentworth Institute of Technology October 11, 2012. Table of Contents. Abstract Introduction to Gossiping The Model Solution Conclusions Citations. Abstract.

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Gossiping

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  1. Gossiping Tam Phuong Nguyen Wentworth Institute of Technology October 11, 2012

  2. Table of Contents • Abstract • Introduction to Gossiping • The Model • Solution • Conclusions • Citations

  3. Abstract • The problem is a common example of gossiping. The model is about women who each know a secret and to see how long it takes for them to know everyone's secrets. I discovered from my research that Gossiping was introduced in discrete mathematics and other applications including communications and distributed memory multiprocessor systems.

  4. What is Gossiping? • In gossiping, each person in the network knows a unique item of info and needs to communicate it to everyone else. (Hedetniemi et al. 1988).

  5. The Model • "There are n ladies and each of them knows an item of gossip not known to the others. They communicate by telephone, and whenever one lady calls another, they tell each other all that they know at a time. How many calls are required before each gossiper knows everything?" (Baker).

  6. Solution • "Let f(n) be the minimum number of calls needed for n people. So f(1)=0, f(2)=1, f(3)=3, and f(4)=4. If n>4 then the equation is f(n)=2n-4. And the solution is that if one of the four women first calls each of the remaining n-4 gossipers, then the four learn of each other's as well as everyone else's information in four calls (as f(4)=4), and then in conclusion one of the four callers calls each of the other women gossipers." (Baker).

  7. Conclusions • In gossiping, every person knows a distinct secret and needs to tell everyone else. • It was originally introduced in discrete mathematics. • The most common example is the telephone one where a person who's a secret and it is their job to tell everyone else, and the point is to see how many calls it takes for everyone to know the secret.

  8. Citations • Brenda Baker, Robert Shostak, “Gossips and Telephones, Discrete Mathematics 2 (1972)” 191-193 MR 46 $#68$. • Bermond J., Gargano, L., Rescigno, A. and Vacarro, U. "Fast Gossiping by Short Messages.” SIAM J. Comput. 27, 917-941,1998. • Hedetniemi, Liestman, A. "A Survey of Gossiping and Broadcasting in Communication Networks.” Networks 18, 319-349, 1988.

  9. The End  Thank You For Your Attention!

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