A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Nonnegative integral subset representations of integer sets
Information Processing Letters
Generalized geometric approaches for leaf sequencing problems in radiation therapy
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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
Algorithmics in intensity-modulated radiation therapy
Algorithms and theory of computation handbook
A note on improving the performance of approximation algorithms for radiation therapy
Information Processing Letters
Faster optimal algorithms for segment minimization with small maximal value
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Faster optimal algorithms for segment minimization with small maximal value
Discrete Applied Mathematics
On explaining integer vectors by few homogenous segments
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Hi-index | 0.89 |
Intensity modulated radiation therapy (IMRT) is one of the most effective modalities for modern cancer treatment. The key to successful IMRT treatment hinges on the delivery of a two-dimensional discrete radiation intensity matrix using a device called a multileaf collimator (MLC). Mathematically, the delivery of an intensity matrix using an MLC can be viewed as the problem of representing a non-negative integral matrix (i.e., the intensity matrix) by a linear combination of certain special non-negative integral matrices called segments, where each such segment corresponds to one of the allowed states of the MLC. The problem of representing the intensity matrix with the minimum number of segments is known to be NP-complete. In this paper, we present two approximation algorithms for this matrix representation problem. To the best of our knowledge, these are the first algorithms to achieve non-trivial performance guarantees for multi-row intensity matrices.