Help me recognize classical problem in task

There is a task. For given lattice (isotropic discrete abelian group ) in R^3 for every vertice y let M(y) - set of neighbour vertices (not necessarily closest one's, for other vertice z: M(z)=M(y)+(z-y)={a+z=y| a \in M(y)}).

Find a mininmal with respect to cardinal subset B(y) of M(y) such that for every x \in M(y) :

B(y) \intersection B(x) isn't empty. (B(x)=B(y)+(x-y) - again isotropical translation).

It seems to be NP problem but in which cases it could be solved

or at least equivalent tasks couldn't be obtained.

Re: Help me recognize classical problem in task

Quote:

Originally Posted by

**icegood**
There is a task.

I don't understand your formalism. Please explain the problem in layman terms without the abstract lingo. Preferably with an example. And where's the algorithm?

Also, the fact that a problem is NP complete doesn't mean it cannot be solved. It can, only not in polynominal time.