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:


Could you help me to write constraint that I mentioned?

  • 2
    $\begingroup$ Can you please provide more context? What do you mean 20m circle? Why doesn't Sudoku work here? $\endgroup$ Commented Jul 2 at 14:42
  • $\begingroup$ 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. $\endgroup$
    – Serkan
    Commented Jul 3 at 7:19

1 Answer 1


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 $$x_{ik} + x_{jk} \le 1 \quad \text{for all $k$}$$


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