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Topic: How to find a bounding line?
Replies: 39   Last Post: Jul 12, 2013 5:39 AM

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 quasi Posts: 12,023 Registered: 7/15/05
Re: How to find a bounding line?
Posted: Jul 7, 2013 8:36 PM

quasi wrote:
>ols6000 wrote:
>

>>I have a N points (x_i, y_i). I want to find a bounding line
>>
>> y = ax + b,
>>
>>such that y_i - y(x_i) >= 0.
>>
>>x_i and y_i are positive integers;
>>a, b and y are real,and x is an integer.
>>y_i = i, and x_{i+1} > x_i for all i<N
>>
>>N is very large (100,000 - 1,000,000), so I'm looking for a
>>method that is O(N) (or better).
>>
>>An ideas on how this line could be found, i e, how to determine
>>a and b efficiently from the N data points?

>
>If the only requirement is that y = ax + b is an upper bounding
>line, you can choose one of a,b arbitrarily. A value for the
>other parameter can then be easily found.
>
>For example, choose b = 0. Then simply choose a as the maximum
>value of y_i/x_i, for i = 1..N.
>
>As another example, choose a = 0. Then simply choose b as the
>maximum value of y_i for i = 1..N.
>
>Thus, you probably want to specify additional conditions on
>the line y = ax + b, other than just an upper bounding line.

Ok, I see you amended your specification.

Now it makes more sense.

quasi

Date Subject Author
7/7/13 Woody
7/7/13 Scott Berg
7/7/13 Peter Percival
7/7/13 Woody
7/7/13 quasi
7/7/13 quasi
7/8/13 quasi
7/8/13 Woody
7/8/13 quasi
7/8/13 LudovicoVan
7/8/13 LudovicoVan
7/10/13 Woody
7/10/13 quasi
7/8/13 Leon Aigret
7/8/13 Woody
7/10/13 Leon Aigret
7/10/13 Leon Aigret
7/10/13 Woody
7/10/13 RGVickson@shaw.ca
7/10/13 Woody
7/10/13 quasi
7/7/13 quasi
7/7/13 quasi
7/7/13 quasi
7/8/13 William Elliot
7/8/13 Peter Percival
7/8/13 quasi
7/11/13 Woody
7/11/13 quasi
7/11/13 LudovicoVan
7/11/13 quasi
7/11/13 Leon Aigret
7/11/13 Woody
7/11/13 Leon Aigret
7/12/13 Woody
7/12/13 Leon Aigret
7/11/13 Woody
7/12/13 quasi
7/12/13 Woody
7/12/13 quasi