Integer and combinatorial optimization
Integer and combinatorial optimization
On decomposing polygons into uniformly monotone parts
Information Processing Letters
SIAM Journal on Discrete Mathematics
Optimal quantization by matrix searching
Journal of Algorithms
Resource-constrained geometric network optimization
Proceedings of the fourteenth annual symposium on Computational geometry
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Robotic Radiosurgery with Beams of Adaptable Shapes
CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for minimizing segments in radiation therapy
Information Processing Letters
Notes on searching in multidimensional monotone arrays
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Decomposition of integer matrices and multileaf collimator sequencing
Discrete Applied Mathematics
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Multicommodity demand flow in a tree
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Geometric algorithms for the constrained 1-D K-means clustering problems and IMRT applications
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Efficient algorithms for intensity map splitting problems in radiation therapy
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Minimizing setup and beam-on times in radiation therapy
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Field splitting problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique aiming to deliver a prescribed conformal radiation dose to a target tumor while sparing the surrounding normal tissues and critical structures. In this chapter, we consider a set of combinatorial and geometric problems that arise in IMRT planning and delivery: (1) the static leaf sequencing problem, (2) the static leaf sequencing with error control problem, (3) the field splitting problem, (4) the dose simplification problem, (5) the dynamic leaf sequencing problem, and (6) the single-arc leaf sequencing problem. We discuss new efficient algorithms for these problems. The main ideas of the algorithms are to exploit the underlying geometric and combinatorial properties of the problems and transform them into graph problems such as shortest paths, optimal matchings, maximum flows, multicommodity demand flows, or linear programming problems. Some open problems and promising directions for future research are also given.