Minimizing the number of apertures in multileaf collimator sequencing with field splitting

Baatar, Davaatseren and Ehrgott, Matthias and Hamacher, Horst W. and Raschendorfer, Ines M (2018) Minimizing the number of apertures in multileaf collimator sequencing with field splitting. Discrete Applied Mathematics, 250. pp. 87-103. ISSN 0166-218X

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In this paper we consider the problem of decomposing a given integer matrix A into an integer conic combination of consecutive-ones matrices with a bound on the number of columns per matrix. This problem is of relevance in the realization stage of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf collimators with limited width. Constrained and unconstrained versions of the problem with the objectives of minimizing beam-on time and decomposition cardinality are considered. We introduce a new approach which can be used to find the minimum beam-on time for both constrained and unconstrained versions of the problem. The decomposition cardinality problem is shown to be NP-hard and an approach is proposed to solve the lexicographic decomposition problem of minimizing the decomposition cardinality subject to optimal beam-on time.

Item Type:
Journal Article
Journal or Publication Title:
Discrete Applied Mathematics
Additional Information:
This is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 250, 2018 DOI: 10.1016/j.dam.2018.04.016
Uncontrolled Keywords:
?? intensity modulated radiation therapymultileaf collimator sequencingfield splittingbeam-on timedecomposition cardinalitymathematics(all)discrete mathematics and combinatoricsapplied mathematicsdiscipline-based research ??
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Deposited On:
16 May 2018 15:22
Last Modified:
09 Apr 2024 23:58