TY  - BOOK
AU  - Kalinowski, Thomas
PY  - 2004
DA  - 2004//
TI  - The  algorithmic complexity of the minimization of the number of segments in multileaf collimator field segmentation
T3  - Preprints aus dem Institut für Mathematik
CY  - Germany; Rostock
AB  - Intensity maps are nonnegative matrices describing the 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 [9] heuristic for the reduction of the number of segments.<eng>
UR  - https://purl.uni-rostock.de/rosdok/id00005903
UR  - https://doi.org/10.18453/rosdok_id00005903
DO  - 10.18453/rosdok_id00005903
LA  - English
N1  - Thomas Kalinowski
ID  - 1987274040
ER  -