to maximize the minimum distance between any two points:-> to maximize the minimum distance between adjacent points -> for this all points must be equally spaced.
hence, choose 'n' equally spaced points in the range (r1, r2) starting from r1 and ending at r2. 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 > > > > > -- "Reduce, Reuse and Recycle" Regards, Vivek.S --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---