Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Integer and combinatorial optimization
Integer and combinatorial optimization
Geometric algorithms for static leaf sequencing problems in radiation therapy
Proceedings of the nineteenth annual symposium on Computational geometry
Mountain reduction, block matching, and applications in intensity-modulated radiation therapy
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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
Optimal Field Splitting, with Applications in Intensity-Modulated Radiation Therapy
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
New algorithm for field splitting in radiation therapy
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Algorithmics in intensity-modulated radiation therapy
Algorithms and theory of computation handbook
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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Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique that delivers prescribed radiation dose distributions, called intensity maps (IMs), to target tumors via the help of a device called the multileaf collimator (MLC). Due to the maximum leaf spread constraint of the MLCs, IMs whose widths exceed a given threshold cannot be delivered as a whole, and thus must be split into multiple subfields. Field splitting problems in IMRTnormally aim to minimize the total beam-on time (i.e., the total time when a patient is exposed to actual radiation during the delivery) of the resulting subfields. In this paper, we present efficient polynomial time algorithms for two general field splitting problems with guaranteed output optimality. Our algorithms are based on interesting observations and analysis, as well as new techniques and modelings. We formulate the first field splitting problem as a special integer linear programming (ILP) problem that can be solved optimally by linear programming due to its geometry; from an optimal integer solution for the ILP, we compute an optimal field splitting by solving a set of shortest path problems on graphs. We tackle the second field splitting problem by using a novel path-sweeping technique on IMs.