**MSC:**- 92C50 Medical applications (general)
- 90C60 Abstract computational complexity for mathematical programming problems, See also {68Q25}

intensity modulation of beams in radiotherapy. In order to

use a multileaf collimator in the static mode for the

realization of the intensity modulation one has to

determine a segmentation, i.e. a representation of an

intensity map as a positive combination of special matrices

corresponding to fixed positions of the multileaf collimator,

called segments. We consider the problem to construct

segmentations with the minimal total number of monitor units

and the minimal number of segments. Neglecting machine--

dependent constraints like the interleaf collision constraint

and assuming that the entries of the intensity map are

bounded by a constant, we prove that a segmentation with

minimal number of segments under the condition that the

number of monitor units is minimal, can be determined in

time polynomial in the matrix dimensions. The results of

our algorithm are compared with Engel's \cite{Eng02}

heuristic for the reduction of the number of segments.