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The possibility of multiple locally optimal dose distributions in radiation treatmentplanning has been discussed and documented in the literature. Here we study a different questionrelated to uniqueness: Is it possible for different treatment plans to generate the same dosedistribution? For greatly simplified two-dimensional model problems, we show that the answeris ‘yes’ in regions where two or ... read moremore beams intersect. In realistic problems, those are of coursenot the only regions of interest. However, as a result of cancellations in regions of intersection,substantial perturbations of beam profiles in certain directions may still have only small effectson the dose distribution. This is interesting because it offers an opportunity to optimize someother useful property, for instance simplicity, among all treatment plans generating a desired dosedistribution with sufficient accuracy. We take a first step beyond our model problems by proving thestability of our results with respect to small perturbations of problem parameters. Since realisticproblems differ from our model problems by much more than small perturbations, we plan topresent a numerical study of more realistic examples in a sequel to this article.read less
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