# MILP Model for Assigning Unique Number for Each Point

I am trying to solve a problem which is smilar to sudoku. I have a specific device location on map I need to gave them a unique integer numbers. However, as in the sudoku I can assign up to 9 and adjacent points cannot has the same number. (for instance inside the 20m circle.) Obviously, I don't have objective function. When it comes to constraint I'm stuck on providing adjacent point unique number issue.

I search couple of article here is the one of them:

https://towardsdatascience.com/using-integer-linear-programming-to-solve-sudoku-puzzles-15e9d2a70baa

Could you help me to write constraint that I mentioned?

• Can you please provide more context? What do you mean 20m circle? Why doesn't Sudoku work here? Commented Jul 2 at 14:42
• For each row and coloumn we can use the number only one time. However in my case I can write as many as I can except the point coverage area is not intersecting. You can think that it is a kind of circle and if circles has intersection area unique numbers cannot be same. Commented Jul 3 at 7:19

For each point $$i$$ and each value $$k\in\{1,\dots,9\}$$, let binary decision variable $$x_{ik}$$ indicate whether point $$i$$ is assigned value $$k$$. If you want to prevent points $$i$$ and $$j$$ from being assigned the same value, impose "conflict" constraints $$x_{ik} + x_{jk} \le 1 \quad \text{for all k}$$