Discrete Mathematics
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Discrete Applied Mathematics
Nonnegative integral subset representations of integer sets
Information Processing Letters
Selected Topics in Column Generation
Operations Research
Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Computers and Operations Research
On the choice of explicit stabilizing terms in column generation
Discrete Applied Mathematics
The sum-of-increments constraint in the consecutive-ones matrix decomposition problem
Proceedings of the 2009 ACM symposium on Applied Computing
A Shortest Path-Based Approach to the Multileaf Collimator Sequencing Problem
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Decomposition of integer matrices and multileaf collimator sequencing
Discrete Applied Mathematics
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Discrete Applied Mathematics
Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning
Operations Research
Shorter path constraints for the resource constrained shortest path problem
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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
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 multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms.