Approximation algorithms for minimizing segments in radiation therapy
Information Processing Letters
The sum-of-increments constraint in the consecutive-ones matrix decomposition problem
Proceedings of the 2009 ACM symposium on Applied Computing
Decomposition of integer matrices and multileaf collimator sequencing
Discrete Applied Mathematics
Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning
Operations Research
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
Hybrid methods for the multileaf collimator sequencing problem
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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
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The segment minimization problem consists of representing an integer matrix as the sum of the fewest number of integer matrices each of which have the property that the non-zeroes in each row are consecutive. This has direct applications to an effective form of cancer treatment. Using several insights, we extend previous results to obtain constant-factor improvements in the approximation guarantees. We show that these improvements yield better performance by providing an experimental evaluation of all known approximation algorithms using both synthetic and real-world clinical data. Our algorithms are superior for 76% of instances and we argue for their utility alongside the heuristic approaches used in practice.