10.18453/rosdok_id00005912 Kalinowski, Thomas Thomas Kalinowski http://d-nb.info/gnd/128420251 https://orcid.org/0000-0002-8444-6848 University of Rostock, Institute of Mathematics 2003 510 Mathematics 2003 en https://purl.uni-rostock.de/rosdok/id00005912 urn:nbn:de:gbv:28-rosdok_id00005912-8 Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is 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 of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of [5] so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.