Minimum \(d\)-convex partition of a multidimensional polyhedron with holes (Q1022895)

Let \(P^3\) be an open polyhedron in the Euclidean space \(E^3\) with polyhedral holes and the edges parallel to the coordinate axes of \(E^3\), where the holes can be of dimension 3, 2, 1, 0. A formula expressing the minimum number of parallelepipeds \(q(P^3)\) into which the polyhedron \(P^3\) can be partitioned has been proposed by the author in [An. Ştiinţ. Fac. Mat. Inform., Univ. Stat Mold. 2, No.~1, 85--88 (2000; Zbl 0996.52008)]. The author studies here the problem of determining the minimum number of \(d\)-convex pieces into which a geometric \(n\)-dimensional polyhedron with holes can be partitioned.