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- W2611281004 abstract "In this research we consider the opimization framework of partitioning a non-negative real matrix A (may be higher dimensional) into binary matrices S1, S2, ... , Sn (i.e., A = Sni=1aiSi , where α1, ...αn are positive real numbers). Our optimization problem can be stated as follows: Minimize, subject to appropriate constraints, f1( S1, ... ,Sn) + f 2(α1, ..., αn) + f3(n) + e(A − Sni=1aiSi ), where f1, f2, f3 are objective terms involving subsets of the variables and e is a penalty term on the error of the partition. These partitioning problems are generally NP-hard and one has to depend on effective heuristic algorithms to find approximate solutions. Our applications are in grid partitioning problems in higher-dimensional domains and segmentation problems in Intensity Modulated Radiation Therapy (IMRT) including Intensity Modulated Arc Therapy (IMAT). In higher-dimensional domains, we use f1 (i.e., f2 = f 3 = e = 0) which corresponds to perimeter or surface area as the objective function. In radiation therapy, we use f 2 and f3 to represent the treatment time and f1 to represent delivery quality. In these applications, we also construct useful lower bounds to assess solution quality." @default.
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- W2611281004 date "2008-01-01" @default.
- W2611281004 modified "2023-09-27" @default.
- W2611281004 title "Approximating optimal partitions: efficient algorithms for higher-dimensional domain decomposition and intensity modulated radiation therapy" @default.
- W2611281004 hasPublicationYear "2008" @default.
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