# Solving the Set Mapping Problem: How Many Is Enough?

• b-boy
In summary, if you have two sets of numbers, and you want to assign each number from one set to two closest numbers from another set, you would use the "an element from B and compare it to each element in A pick two closest" approach. This would let you select more than two values, but it wouldn't solve the problem in a meaningful way.
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.

b-boy said:
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.

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.

## 1. What is the Set Mapping Problem?

The Set Mapping Problem is a mathematical problem that involves determining the minimum number of elements needed to map one set onto another. It is often used in computer science and operations research to optimize processes and solve optimization problems.

## 2. Why is the Set Mapping Problem important?

The Set Mapping Problem is important because it allows us to find the most efficient and effective way to map one set onto another. This can be useful in various real-world applications, such as supply chain management, scheduling, and resource allocation.

## 3. How is the Set Mapping Problem solved?

The Set Mapping Problem can be solved using various mathematical techniques, such as linear programming, graph theory, and combinatorics. The specific approach will depend on the specific problem at hand and the constraints involved.

## 4. What factors influence the number of elements needed to solve the Set Mapping Problem?

The number of elements needed to solve the Set Mapping Problem can be influenced by various factors, including the size and complexity of the two sets, the type of mapping or transformation required, and any constraints or limitations on the problem.

## 5. What are some real-world applications of the Set Mapping Problem?

The Set Mapping Problem has many real-world applications, including resource allocation in project management, optimizing supply chain networks, and scheduling tasks in manufacturing or transportation. It can also be used in data analysis and machine learning to find the most efficient way to map data onto a model or algorithm.

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