Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Geometric algorithms for static leaf sequencing problems in radiation therapy
Proceedings of the nineteenth annual symposium on Computational geometry
Mountain reduction, block matching, and applications in intensity-modulated radiation therapy
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Approximation algorithms for minimizing segments in 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
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The 3-D static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to deliver a prescribed radiation dose to a target tumor accurately and efficiently The treatment time and machine delivery error are two crucial factors of a solution (i.e., a treatment plan) for the SLS problem In this paper, we prove that the 3-D SLS problem is NP-hard, and present the first ever algorithm for the 3-D SLS problem that can determine a tradeoff between the treatment time and machine delivery error (also called the “tongue-and-groove” error in medical literature) Our new 3-D SLS algorithm with error control gives the users (e.g., physicians) the option of specifying a machine delivery error bound, and subject to the given error bound, the algorithm computes a treatment plan with the minimum treatment time We formulate the SLS problem with error control as computing a k-weight shortest path in a directed graph and build the graph by computing g-matchings and minimum cost flows Further, we extend our 3-D SLS algorithm to the popular radiotherapy machine models with different constraints In our extensions, we model the SLS problems for some of the radiotherapy systems as computing a minimum g-path cover of a directed acyclic graph We implemented our new 3-D SLS algorithm suite and conducted an extensive comparison study with commercial planning systems and well-known algorithms in medical literature Some of our experimental results based on real medical data are presented.