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

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<mark>Journal publication date</mark>11/12/2018
<mark>Journal</mark>Discrete Applied Mathematics
Volume250
Number of pages17
Pages (from-to)87-103
Publication statusPublished
Early online date18/05/18
Original languageEnglish

Abstract

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.

Bibliographic note

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