An almost linear time algorithm for generalized matrix searching
SIAM Journal on Discrete Mathematics
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Mathematical Programming: Series A and B
Geometric algorithms for static leaf sequencing problems in radiation therapy
Proceedings of the nineteenth annual symposium on Computational geometry
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
On Steepest Descent Algorithms for Discrete Convex Functions
SIAM Journal on Optimization
New algorithm for field splitting in radiation therapy
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Efficient algorithms for intensity map splitting problems in radiation therapy
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Field splitting problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A new field splitting algorithm for intensity-modulated radiation therapy
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multileaf collimator (MLC) with amaximum leaf spread constraint is used to deliver the prescribed radiation intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large IM into several overlapping sub-IMs with each being delivered separately. We develop an efficient algorithm for solving the field splitting problem while minimizing the total variation of the resulting sub-IMs, thus improving the treatment delivery efficiency.Our basic idea is to formulate the field splitting problemas computing a shortest path in a directed acyclic graph, which expresses a special "layered" structure. The edge weights in the graph can be computed by solving an optimal vector decomposition problem using local searching and the proximity scaling technique as we can prove the L-convexity and totally unimodularity of the problem. Moreover, the edge weights of the graph satisfy the Monge property, which enables us to solve this shortest path problem by examining only a small portion of the graph, yielding a time-efficient algorithm.