Reducing the tongue–and–groove underdosage in MLC shape matrix decomposition

We present an algorithm for optimal step-and-shoot multileaf collimator field segmentation minimizing tongue-and-groove effects. Adapting the concepts of [7] we characterize the minimal decomposition time as the maximal weight of a path in a properly constructed weighted digraph. We also show that this decomposition time can be realized by a unidirectional plan, thus proving that the algorithm from [9] is monitor unit optimal in general and not only for unidirectional leaf movement. Our characterization of the minimal decomposition time has the advantage that it can be used to derive a heuristic for the reduction of the number of shape matrices following the ideas of [7]