Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 quasi Posts: 12,067 Registered: 7/15/05
Re: How to find a bounding line?
Posted: Jul 7, 2013 8:59 PM

quasi wrote:
>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.

Also, now that I look more carefully, it appears you want a
lower bounding line, not an upper bounding line.

No problem.

I definitely see an O(N^2) approach, but in fact, I think I see
an O(N) approach. If my idea survives further scrutiny, I'll
post it in my next reply.

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