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Any help appreciated

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- Thread starter NotASmurf
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In summary, the conversation discusses finding a function for a set of real numbers that maps to a single number, with the goal of optimizing time complexity in a computational context. One suggestion is to use injective functions, which can be messy and require infinite precision. Another suggestion is to use a function that maps rational numbers to rational numbers. The conversation also mentions the idea of using strings as labels, but this may not be practical due to increased processing requirements.

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Any help appreciated

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What's your domain and codomain?

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- #4

Mentor

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More context would help, but I guess there is an easier solution. Why can't you just use the set of three numbers as label? Expressed as string or whatever if the data format is an issue.

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Science Advisor

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The sets ##\mathbb R^m## and ##\mathbb R^n## have the same cardinality for all ##m,n##

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Mentor

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Your label will have to be longer than the length of a single coordinate, in a suitable format. If you have N possible values for the single coordinate, you need N

I don't see how concatenating strings would increase the time complexity of anything.

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In any case, given ##m/n## and ##m'/n'## in reduced form (meaning that ##m## and ##n## have no common divisors and ##n>0## and likewise for ##m'## and ##n'##), you can send this to ##2^m 3^n 5^{m'} 7^{n'}##.

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mfb said:I don't see how concatenating strings would increase the time complexity of anything.

The processing required for what those strings will be processed as it will

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What's $$ m' $$ and $$n'$$?micromass said:

In any case, given ##m/n## and ##m'/n'## in reduced form (meaning that ##m## and ##n## have no common divisors and ##n>0## and likewise for ##m'## and ##n'##), you can send this to ##2^m 3^n 5^{m'} 7^{n'}##.

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It is linear in the number of vertices, which is as good as it can get.NotASmurf said:The processing required for what those strings will be processed as it will

m' and n' are the numerator and denominator of the second fraction.

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