Solving the Set Mapping Problem: How Many Is Enough?

[b-boy]

Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A. this way i would gat a subset of B assigned to each A element for which i can the alpply the initaill approach. My question now is:

"... i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A." is two enough. Obviously not but what is ?? How do i calculate/prove that ??

thnx

b-boy

PS

this is my first post so please help me improve my question if it is not clear enough.

 

[Erland]

Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A. this way i would gat a subset of B assigned to each A element for which i can the alpply the initaill approach. My question now is:

"... i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A." is two enough. Obviously not but what is ?? How do i calculate/prove that ??

thnx

b-boy

PS

this is my first post so please help me improve my question if it is not clear enough.

Hmm... say you have A={1,2,3,4}, B={5,6,7,8}. Call your first assignment function F.

Then F(1)=F(2)=F(3)=F(4)={5,6}.

Now, call your second assignment function G. Then G(1)=G(2)=ø and G(3)=G(4)={5,6,7,8}, if I understand you correctly.

So, this latter would not assign any values to 1 and 2, and all values are assigned to 3 and 4.

To let G select more than 2 values would not solve the problem in a meaningful way either, as I understand it.

 

[b-boy]

yes you understood me correctly and pointed out something that i did not see. My cases were ususly two uniformly (more or less) distributed sets. A= {1,3,5,7} and B = {2,4,6,8} and A <<B. but now when you pointed the flaw in my logic i have to reconsider my problem , thank you.