It is not a solution for minimize maximum distance either, since |x(i)-x(j)|
<= c does not hold for every pair of points, only for adjacent points.
2009/10/21 saltycookie <saltycoo...@gmail.com>
> Yes, you are quite right. If I am not mistaken, you give a good solution
> for finding the minimum maximum distance.
>
> But what about the original problem where we want to find the maximum
> minimum distance? I am not clear about the connection between the two
> problems.
>
> Thanks.
>
> 2009/10/21 Dave <dave_and_da...@juno.com>
>
>
>> 林夏祥 , think again. If we are trying to minimize the maximum distance,
>> then we want to minimize the upper bound. That is what I specified:
>> letting c be the upper bound, find the smallest c such that all of the
>> distances do not exceed c. That gives rise to the inequalities
>> |x(i)-x(j)| <= c.
>> If necessary, this can be written as two inequalities:
>> x(i) - x(j) <= c and
>> x(j) - x(i) <= c.
>>
>> Since the relationship is "and," we can just use the two inequalities
>> as part of the constraint conditions.
>>
>> Dave
>>
>> On Oct 21, 12:02 am, 林夏祥 <saltycoo...@gmail.com> wrote:
>> > I don't think LP can solve it. We are to maximize c, not minimize c.
>> > The formulas we have are:
>> >
>> > |x(i)-x(j)| >= c for all i and j
>> > r1(i) <= x(i) <= r2(i) for all i
>> > The first inequality actually is combination of two linear equalities:
>> x(i)
>> > - x(j) >= c or x(i) - x(j) <= -c. Notice the relation of the two is
>> "or",
>> > and we cannot put them together to get a system of linear inequalities.
>> > 2009/10/21 Dave <dave_and_da...@juno.com>
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> > > This is a linear programming problem. The way you formulate the
>> > > problem depends on the capabilities of the linear programming software
>> > > you have.
>> >
>> > > Basically, you want to
>> > > minimize c
>> > > by finding x(1) to x(n) such that
>> >
>> > > |x(i)-x(j)| <= c for all i and j
>> > > r1(i) <= x(i) <= r2(i) for all i
>> >
>> > > Dave
>> >
>> > > On Oct 5, 9:22 am, monty 1987 <1986mo...@gmail.com> wrote:
>> > > > We have to locate n points on the x-axis
>> > > > For each point xi
>> > > > the x co-ordinate of it lies between a
>> range
>> > > > [r1i,r2i]
>> > > > Now we have to decide the location of points such that
>> > > > minimum { distance between any two points } is maximum.
>> >
>> > > > Any answer is welcomed.
>> >
>> > --
>> > 此致
>> > 敬礼！
>> >
>> > 林夏祥- Hide quoted text -
>> >
>> > - Show quoted text -
>> >>
>>
>
>
> --
> 此致
> 敬礼！
>
> 林夏祥
>
--
此致
敬礼！
林夏祥
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