A minimum cost flow formulation for approximated MLC segmentation

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be written as a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem to find an approximation B of A satisfying prescribed upper and lower bounds for each entry. The approximation B is determined such that the corresponding fluence can be realized with a prescribed delivery time using a multileaf collimator with interleaf collision constraint, and under this condition the distnace between A and B is minimized.