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Saturday, July 21, 2007

When Math is Misused - Revenge

It's revenge time. You should have read the last post on the same topic. I've got the chance to write a paper and I just wanted to see how it feels like to write such complicated mathematical stuff. The paper was about a min-heap and stuff, pretty simple and can be written in a few paragraphs. Take a look at the pictures.
The amazing thing is that after the 2 days I spent writing in 2 pages, I realized that well-formalizing the issue allowed for much much more potential that was initially possible. Initially we just move the load from a loaded machine to the lightest node in the system, but after well-formalizing the problem it is now possible to prove the degree to which this algorithm is really effective and efficient or not. It also showed me a point I didn't look to before, that if a machine get lightly loaded, it can take the load from other machines, without the need of the other machines to ask it to, and thus making real load-balancing.
I really was amazed not only because of the new potentials, but also that writing mathematic proofs and well-formalization is very much like programming, the logic of the proof follows like lines of code follows for the goal of the program/proof. I can say that I enjoyed writing that paper, well, like I do enjoy writing complex C++ code (and I do enjoy that more than games) (maybe it is cause I used the paper to learn Latex, I dunno).

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