| Summary: | We consider the problem of finding a position of a <i>d</i>-dimensional box with given edge lengths that maximizes the number of enclosed points of the given finite set <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mo>⊂</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>d</mi> </msup> </mrow> </semantics> </math> </inline-formula>, i.e., the problem of optimal box positioning. We prove that while this problem is polynomial for fixed values of <i>d</i>, it is NP-hard in the general case. The proof is based on a polynomial reduction technique applied to the considered problem and the 3-CNF satisfiability problem.
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