Abstract
In this paper, we study an optimization problem, called the circular matrix-merging (CMM) problem: Given a cyclic sequence of n non-negative matrices that are associated with some locations on a circle and an operation that merges two consecutive matrices into one matrix at the expense of some merging error, merge the n matrices into the minimum number of matrices under the constraint of a threshold of the total merging error. This problem arises in Volumetric Intensity-Modulated Arc Therapy (VMAT) for radiation cancer treatment, where the circular structure represents a delivery arc path of 360° around the patient and the matrices represent the radiation fluence maps at selected delivery angles on that path. By computing the minimum k matrices, the CMM algorithm produces a most efficient delivery plan that meets clinical requirements. Based on dynamic programming and computing a set of k-link shortest paths, we present a polynomial time algorithm for the CMM problem, improving the quality and efficiency of VMAT delivery.
This research was supported in part by NSF under Grant CCF-1217906.
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Chen, D.Z., Craft, D., Yang, L. (2014). A Circular Matrix-Merging Algorithm with Application in VMAT Radiation Therapy. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_4
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DOI: https://doi.org/10.1007/978-3-319-08016-1_4
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