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How to waste time trying to solve a problem that even a child can prove you it can't be done...

At least now I want to continue writing on this blog.... I have messed up in the past trying to solve the wrong problem, solve the problem in a wrong way, or trying to solve a problem that can't be solved. So this time I simplify the problem and made sure that there is a answer. But again I failed after 1 week because..... This is what happened......

We were trying to see whether forming a circular link in a sensor network can reduce the overall energy consumption. I did the calculation for a simplified case & figured out it can be done, if two nodes that wants to talk to each other is within a certain angle. Then I tried to solve the big problem by integrating over the whole sensor region. However I got stuck. I then went and talk to my supervisor and discussed about the problem. He said "we don't know whether nodes will follow the shorter or longer path along the circular link, so lets assume it goes through a shorter path 1/2 the time and 1/2 it goes through the longer path". It was more general than the specific angle that I derived and seams to be attractive. Fine, I'll go ahead & solve the problem again by integrating. After wasting a week (well I didn't remember integration much so had to do some background reading) I realized there is no solution & routing through the circular link is worse. Where things go wrong? Well, when my supervisor suggest the change, I never went back and did the calculation for the simplified case. In three lines it can be proven that the new solution won't work (a kid who has a basic idea on geometry will prove this to me).

Lesson Learned:
  1. Do a simple calculation for boundary conditions
  2. If it works go for the general case
  3. If you do any changes in the middle make sure to do the simple calculation again (step 1)
  4. Repeat step 2 and 3 until you are completely done
Well I at least I learn integration so one week is not totally lost....

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