Abstract
In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multi-leaf collimator (MLC) is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large intensity map into several overlapping sub-IMs. We develop the first optimal linear time algorithm for solving the field splitting problem while minimizing the total complexity of the resulting sub-IMs. Meanwhile, our algorithm strives to minimize the maximum beam-on time of those sub-IMs. Our basic idea is to formulate the field splitting problem as computing a shortest path in a directed acyclic graph, with a special “layered” structure. The edge weights of the graph satisfy the Monge property, which enables us to speed up the algorithm to optimal linear time. To minimize the maximum beam-on time of the resulting sub-IMs, we consider an interesting min-max slope path problem in a monotone polygon which is solvable in linear time. The min-max slope path problem is of its own interest.
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Wu, X., Dou, X., Bayouth, J., Buatti, J. (2007). New Algorithm for Field Splitting in Radiation Therapy. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_60
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DOI: https://doi.org/10.1007/978-3-540-77120-3_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77118-0
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