10.18453/rosdok_id00005901 Kalinowski, Thomas Thomas Kalinowski http://d-nb.info/gnd/128420251 https://orcid.org/0000-0002-8444-6848 University of Rostock, Institute of Mathematics 2004 510 Mathematics 2004 en https://purl.uni-rostock.de/rosdok/id00005901 urn:nbn:de:gbv:28-rosdok_id00005901-4 We present an algorithm for optimal step-and-shoot intensity modulated radiation therapy without interleaf collision and with elimination of tongue-and-groove effects. Adapting the concepts of [6] we characterize the minimal number of monitor units as the maximal weight of a path in a properly constructed weighted digraph. We also show that this number of monitor units can be realized by an unidirectional plan, thus proving that the algorithm of Kamath et al. [10] is monitor unit optimal in general and not only for unidirectional leaf movement. Our characterization of the minimal number of monitor units has the advantage that it can be used to derive a heuristic for the reduction of the number of segments following the ideas of [7].