Abstract
In this paper we study several rectilinear terrain construction problems, which model the leaf sequencing problems in intensity-modulated radiation therapy (IMRT). We present a novel unified approach based on geometric techniques for solving these terrain construction problems. Our ideas include formulating the terrain construction problems as computing shortest paths in a weighted directed graph and building the graph by computing optimal bipartite matchings on various geometric objects subject to specific constraints of each of the problems. Further, since we need to compute optimal bipartite matchings on many sets of geometric objects, we use techniques for computing such matchings in a batch fashion to speed up these matching computations. Our approach leads to the first algorithms for several leaf sequencing problems in IMRT that are practically fast and guarantee an output which is optimal for a large sub-class of solutions. The previously known leaf sequencing algorithms which are currently used in radiation therapy practice are all heuristics that do not guarantee any good quality of the output solutions and may run in a long time. Our implementation results show that our terrain construction algorithms run very fast on real medical data (all under few seconds).
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Chen, D., Hu, X., Luan, S. et al. Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy. Algorithmica 42, 265–288 (2005). https://doi.org/10.1007/s00453-005-1169-7
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DOI: https://doi.org/10.1007/s00453-005-1169-7