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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: 12,067 Registered: 7/15/05
Re: How to find a bounding line?
Posted: Jul 7, 2013 8:36 PM

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.

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