  The computational complexity of the "cluster minimization problem" is
revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued
that the original NP-hardness proof does not apply to pairwise potentials of
physical interest, such as those that depend on the geometric distance between
the particles. A geometric analog of the original problem is formulated, and a
new proof for such potentials is provided by polynomial time transformation
from the independent set problem for unit disk graphs. Limitations of this
formulation are pointed out, and new subproblems that bear more direct
consequences to the numerical study of clusters are suggested.
