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
Field splitting 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
Efficient intensity map splitting algorithms for intensity-modulated radiation therapy
Information Processing Letters
Optimal Field Splitting, with Applications in Intensity-Modulated Radiation Therapy
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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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) 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.