An Exact Method for the Minimum Cardinality Problem in the Treatment Planning of Intensity-Modulated Radiotherapy

References

• Ahuja R. K., Hamacher H. W. A network flow algorithm to minimize beam-on time for unconstrained multileaf collimator problems in cancer radiation therapy. Networks (2005) 45(1):36–41Crossref, Google Scholar
• Baatar D., Boland N., Brand S., Stuckey P. J. Minimum cardinality matrix decomposition into consecutive-ones matrices: CP and IP approaches. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (2007) 4510(Springer, Berlin) 1–15Lecture Notes in Computer ScienceCrossref, Google Scholar
• Baatar D., Hamacher H. W., Ehrgott M., Woeginger G. J. Decomposition of integer matrices and multileaf collimator sequencing. Discrete Appl. Math. (2005) 152(1–3):6–34Crossref, Google Scholar
• Bansal N., Coppersmith D., Schieber B. Minimizing setup and beam-on times in radiation therapy. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (2006) 4110(Springer, Berlin) 27–38Lecture Notes in Computer ScienceCrossref, Google Scholar
• Collins M. J., Kempe D., Saia J., Young M. Nonnegative integral subset representations of integer sets. Inform. Processing Lett. (2007) 101(3):129–133Crossref, Google Scholar
• Ehrgott M., Hamacher H. W., Nußbaum M., Alves C. J. S., Pardalos P. M., Vicente L. N. Decomposition of matrices and static multileaf collimators: A survey. Optimization in Medicine. Springer Optimization and Its Applications (2008) 12(Springer, New York) 25–46Crossref, Google Scholar
• Engel K. A new algorithm for optimal multileaf collimator field segmentation. Discrete Appl. Math. (2005) 152(1–3):35–51Crossref, Google Scholar
• Kalinowski T. Algorithmic complexity of the minimization of the number of segments in multileaf collimator field segmentation. (2004) . Technical report, Department of Mathematics, University of Rostock, Rostock, GermanyGoogle Scholar
• Langer M., Thai V., Papiez L. Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators. Medical Phys. (2001) 28(12):2450–2458Crossref, Google Scholar
• Luan S., Saia J., Young M. Approximation algorithms for minimizing segments in radiation therapy. Inform. Processing Lett. (2007) 101(6):239–244Crossref, Google Scholar
• Mak V. Iterative variable aggregation and disaggregation in IP: An application. Oper. Res. Lett. (2007) 35(1):36–44Crossref, Google Scholar
• Nußbaum M. Min cardinality C1-decomposition of integer matrices. (2006) . Master's thesis, Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, GermanyGoogle Scholar
• Taşkin Z. C., Smith J. C., Romeijn H. E., Dempsey J. F. Optimal multileaf collimator leaf sequencing in IMRT treatment planning. (2007) . Retrieved September 19, 2008, http://www.ise.ufl.edu/cole/Papers/imrt_unconstrained.pdfGoogle Scholar
• Xia P., Verhey L. J. Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments. Medical Phys. (1998) 25(8):1424–1434Crossref, Google Scholar