An almost linear time algorithm for generalized matrix searching
SIAM Journal on Discrete Mathematics
Geometric algorithms for static leaf sequencing problems in radiation therapy
Proceedings of the nineteenth annual symposium on Computational geometry
Optimal Field Splitting with Feathering in Intensity-Modulated Radiation Therapy
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Efficient algorithms for intensity map splitting problems in radiation therapy
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A new field splitting algorithm for intensity-modulated radiation therapy
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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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) with a maximum leaf spread constraint is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of a MLC may require to split a large intensity map into several overlapping sub-IMs with each being delivered separately. We develop a close-to-linear time algorithm for solving the field splitting problem while minimizing the total complexity of the resulting sub-IMs, thus improving the treatment delivery efficiency. 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, which expresses a special ''layered'' structure. The edge weights of the graph satisfy the Monge property, which enables us to solve this shortest path problem by examining only a small portion of the graph, yielding a close-to-linear time algorithm. 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 may be of interest in its own right. Experimental results based on real medical data and computer generated IMs showed that our new algorithm runs fast and produces high quality field splitting results.