A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Realization of intensity modulated radiation fields using multileaf collimators
General Theory of Information Transfer and Combinatorics
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning
Operations Research
A closest vector problem arising in radiation therapy planning
Journal of Combinatorial Optimization
A shortest path-based approach to the multileaf collimator sequencing problem
Discrete Applied Mathematics
Hybrid methods for the multileaf collimator sequencing problem
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Iterative variable aggregation and disaggregation in IP: An application
Operations Research Letters
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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 Engel [Discrete Appl. Math., in press, doi:10.1016/j.dam.2004.10.007] 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 maximal length of a path in a layered digraph. We derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units, and we propose a heuristic approach to the reduction of the number of segments.