Efficient parallel algorithms for string editing and related problems
SIAM Journal on Computing
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
Notes on searching in multidimensional monotone arrays
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Decomposition of integer matrices and multileaf collimator sequencing
Discrete Applied Mathematics
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Algorithmics in intensity-modulated radiation therapy
Algorithms and theory of computation handbook
Fast coupled path planning: from pseudo-polynomial to polynomial
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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The couple path planning (CPP) problem seeks the motion paths of the leaves of a multileaf collimator, to optimally reproduce the prescribed dose in intensity-modulated radiation therapy (IMRT). We study two versions of the CPP problem, constrained and unconstrained CPP, based on whether the starting and ending locations of the sought paths are prespecified. The unconstrained CPP problem models the leaf sequencing problem in dynamic IMRT delivery, while the set of all constrained CPP problem instances, in which all combinations of the starting and ending locations are considered, plays a key role in an emerging IMRT technique called arc-modulated radiation therapy. We give efficient algorithms for both the constrained and unconstrained CPP problems, and for computing the set of all constrained CPP problem instances. Our results are based on several new ideas and geometric observations, and substantially improve the solutions based on standard techniques. Implementation results show that our CPP algorithms run fast and produce better IMRT treatment plans than current methods.