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Problem Statement:
After optimizing the Alpha value for different regions, when tests were run for targets of various regions, it was observed that results for only North America and Europe were improved and for other regions, Error distance still mounted to thousand of Kilometers. One observation was that this is mainly due to instability of internet connectivity in these regions and better results in Europe and North America are due to better and stable connectivity in those areas. However, another thing observed during the analysis was that these two regions also possess large number of landmarks compared to other regions. So the impact of landmark's density can't be ignored. It was observed that most of the times poor results appear mainly because of the fact that no landmark is found in close vicinity of the target and hence even three final selected landmarks give RTT values above 300ms or so.
So to analyze this geographical distance impact on Error distance, I have conducted a region by region analysis in which I have done following main tasks:
? First, I found distance between different landmarks of a region (their inter-distance) and then calculated the average distance for each region. E.g. if there are 10 landmarks in a certain region, I calculated distance between a landmark and all other landmarks in that region and in this way inter-distance of all landmarks was calculated and then averaging out these results, I got one average distance value for each region.
? Then I took targets of each region, and run tests for them (using average alpha value of that particular region). In this way I got error distance for each target and then we calculated average Error distance for each region.
? Now the analysis began. I wanted to investigate that what behavior will be there in error distance when the average geographical distance is higher and what it will be when average geographical distance is lower. Of course, an ideal situation was that when there is high geographical distance between landmarks, i.e. landmarks are far apart from each other then error distance should be higher compared to the case when we have high number of landmarks in a particular region (i.e. we have low average geographical distance).
? Following table shows the average geographical distance and average error distance for each region.

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Based on the above data, I plotted a graph to see the relationship between distance and error distance in a graphical manner. The graph is shown below:

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