Rights statement: 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
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Minimizing the number of apertures in multileaf collimator sequencing with field splitting
AU - Baatar, Davaatseren
AU - Ehrgott, Matthias
AU - Hamacher, Horst W.
AU - Raschendorfer, Ines M
N1 - 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
PY - 2018/12/11
Y1 - 2018/12/11
N2 - 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 bothconstrained 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.
AB - 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 bothconstrained 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.
KW - Intensity modulated radiation therapy
KW - Multileaf collimator sequencing
KW - Field splitting
KW - Beam-on time
KW - Decomposition cardinality
U2 - 10.1016/j.dam.2018.04.016
DO - 10.1016/j.dam.2018.04.016
M3 - Journal article
VL - 250
SP - 87
EP - 103
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -