Discussion 1

1. Let n be a large number (much larger than 8). One person can add two numbers in Tcomp time and pass a number to a neighbor in Tmess time, and can write and read a number on a blackboard, each in Tshare time. Assume that Tcomp is much smaller than Tshare, and Tshare is much smaller than Tmess. Assume that each person can do only one thing at the time.
   
   1. Eight people are sitting in a ring. There is no blackboard. How long would it take to add n numbers? What do you assume about the initial data distribution?
   2. What if the eight people form a 2 by 4 grid where they can pass numbers to their north, south, east, and west neighbors? There is no wrap around and there is still is no blackboard.
   3. Is there a better configuration than a ring or grid for 8 people? Eg, if all people are directly connected to all people, but can communicate with only one other person at a time (Assume that there is a phone to dial into other person)?
   4. How does the computation change if the eight people have a blackboard that they all can write on and read from? What is now needed to ensure validity of the computation?
   5. If the people are processors, passing a number is communicating over the ethernet, and reading/writing the blackboard is memory access, what are current day numbers for Tcomp, Tmess, and Tshare?
   
   
2. Respond to someone else's solution, and generate a consensus solution to be posted on the main discussion board.