Integer and combinatorial optimization
Integer and combinatorial optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Inverse radiation therapy planning: a multiple objective optimization approach
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Journal of Computer and System Sciences
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
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Multiobjective Decomposition of Positive Integer Matrix: Application to Radiotherapy
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
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
Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning
Operations Research
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
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
A closest vector problem arising in radiation therapy planning
Journal of Combinatorial Optimization
A shortest path-based approach to the multileaf collimator sequencing problem
Discrete Applied Mathematics
Minimum decomposition into convex binary matrices
Discrete Applied Mathematics
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
Iterative variable aggregation and disaggregation in IP: An application
Operations Research Letters
Faster optimal algorithms for segment minimization with small maximal value
Discrete Applied Mathematics
How to decompose a binary matrix into three hv-convex polyominoes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
On explaining integer vectors by few homogenous segments
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Hi-index | 0.05 |
In this paper, we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property. This problem is motivated by an application in cancer radiotherapy planning, namely the sequencing of multileaf collimators to realize a given intensity matrix. In addition, we also mention another application in the design of public transportation. We are interested in two versions of the problem, minimizing the sum of the coefficients in the decomposition (decomposition time) and minimizing the number of matrices used in the decomposition (decomposition cardinality). We present polynomial time algorithms for unconstrained and constrained versions of the decomposition time problem and prove that the (unconstrained) decomposition cardinality problem is strongly NP-hard. For the decomposition cardinality problem, some polynomially solvable special cases are considered and heuristics are proposed for the general case.