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A shortest path-based approach to the multileaf collimator sequencing problem

机译：解决多叶准直仪排序问题的最短路径方法

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摘要

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.
机译：多叶准直仪测序问题是有效治疗癌症的重要组成部分。可以将问题表达为找到将整数矩阵分解为二进制矩阵的加权序列，该二进制矩阵的行满足连续的1属性。最小化分解的基数是一个重要的目标，并且即使对于仅限于单个列或行的矩阵，也显示出强烈的NP难解性。我们表明，在后一种情况下，它可以作为最短路径问题得到有效解决，从而简单证明单行问题在最大强度下是固定参数可处理的。我们利用这一结果开发了新的线性和约束编程模型。我们的方法极大地改善了最著名的问题，使实际大小的问题实例在精确算法的范围内。

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