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18432Re: Real life

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  • Kaveh
    Nov 14, 2006
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      No Ronny. A and B are both "fixed" sets of n and km positive integers,
      and their elements are not arbitrary. The problem is not to construct
      A and B, but to check if their differences cover the range [0,nm].

      Best wishes.


      --- In primenumbers@yahoogroups.com, "Ronny Edler" <ronny.e@...> wrote:
      > > In the real life of computation, my B set is flexible. I should
      > > generate k*m numbers is B until the [0,nm] range is covered. So
      > > actully the real problem is to find optimal k such that the range of
      > > question is covered. But checking the coverage in O(nm) is way too
      > > slow. So I need to resolve this before I can worry about k.
      > To clarify on this: You have a _fixed_ set A and want to construct a
      set B,
      > such that the differences span the
      > interval [0,mn-1], with all members of A and B are in [0,mn-1]?
      > Furthermore, as an answer of your algorithm you need something like:
      > "Here is a set B that satifies the constraints" or "I have proven
      that no
      > such B exists".
      > Well, i think that unless you construct B, testing abitrarily
      generated sets
      > will take you a _long_ time.
      > Example: Take |A| = 3, |B| = 2. There are (6 choose 3) times (6
      choose 2) =
      > 20*15 = 300 possible set combinations.
      > The only working ones are: A = {1,3,5}, B = {0,1} and A = {3,4,5} and
      > B={0,3}.
      > That is 2 out of 300. (m,n are tiny! here)
      > > Ronny, I guess your test will take O(nm) again to guarantee that the
      > > entire range is covered, right?
      > Yes, if you keep track of the numbers you already tested.
      > Ronny
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