Max of Min and Min of Max - 3
We continue this chain .
The basic question was: If a convex region is being cut into n convex pieces such that the maximum(minimum) of some quantity X among the pieces is to be minimized(maximized), will it automatically make the value of X equal among the pieces?
The maximizing the minimum version of this question with say, X being diameter could result in many degenerate (long and infinitely thin) pieces. So, let us ask a tighter version of this same broad question:
If a convex region is to be cut into n convex pieces all of equal area such that the maximum(minimum) of some other quantity X is minimized(maximized) over the n pieces, will the value of X get automatically equalized?
The basic question was: If a convex region is being cut into n convex pieces such that the maximum(minimum) of some quantity X among the pieces is to be minimized(maximized), will it automatically make the value of X equal among the pieces?
The maximizing the minimum version of this question with say, X being diameter could result in many degenerate (long and infinitely thin) pieces. So, let us ask a tighter version of this same broad question:
If a convex region is to be cut into n convex pieces all of equal area such that the maximum(minimum) of some other quantity X is minimized(maximized) over the n pieces, will the value of X get automatically equalized?
posted by R.Nandakumar @ 10:50 PM
0 Comments:
Post a Comment
<< Home