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... .Obviously, this overhead is function of the amount of resources, M, and increasing M, although it provides better knowledge, it results in a larger overhead.

... .Obviously, this overhead is function of the amount of resources, M, and although increasing M provides better efficency, it results in a larger overhead.

Which one between these two sentences sounds better ? Do you have a better formulation ? should I say "a function" or just "function" ?

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Obviously, this overhead is a function of the amount of resources, M, and increasing M, although it provides better knowledge, it results in a larger overhead.

Obviously, this overhead is a function of the amount of resources, M, and although increasing M provides better efficency, it results in a larger overhead.

I'd say the second sentence flows better. It's easier to mentally parse when there's one less comma-separated phrase interrupting you. If you were going to use the first, you should remove the highlighted it. This should not be included since, if you consider the sentence without the parenthetical although it provides better knowledge, it is this:

increasing M it results in a larger overhead.

Which is obviously incorrect, and should be:

increasing M results in a larger overhead.

In the second sentence, this doesn't apply, because the it is part of a separate phrase, and is a placeholder for increasing M. As a side note, efficiency was spelled wrong.

...although increasing M provides better efficiency, [increasing M] results in a larger overhead.

Finally, it should be a function, not function.

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