Intensity modulated radiation therapy (IMRT) is one of the most effective modalities for modern cancer treatment. The key to successful IMRT treatment hinges on the delivery of a two-dimensional discrete radiation intensity matrix using a device called a multileaf collimator (MLC). Mathematically, the delivery of an intensity matrix using an MLC can be viewed as the problem of representing a non-negative integral matrix (i.e., the intensity matrix) by a linear combination of certain special non-negative integral matrices called segments, where each such segment corresponds to one of the allowed states of the MLC. The problem of representing the intensity matrix with the minimum number of segments is known to be NP-complete. In this paper, we present two approximation algorithms for this matrix representation problem. To the best of our knowledge, these are the first algorithms to achieve non-trivial performance guarantees for multi-row intensity matrices. 相似文献
Recently many runoff models based on cellular automaton (CA) have been developed to simulate floods; however, the existing models cannot be readily applied to complex urban environments. This study proposes a novel rainfall-runoff model based on CA (RRCA) to simulate inundation. Its main contributions include a fine runoff generation process that considers 12 urban scenarios rather than a single land use type and the confluence process determined by the new transition rules considering water supply and demand (WS-WD transition rules). RRCA was compared with another CA based flood model (E2DCA). With the benchmark model, the results showed that there was good agreement, with an R-squared greater than 0.9, and that RRCA was more sensitive to waterlogging levels than E2DCA. Furthermore, the simulated vegetation interception, infiltration and drainage processes had varying degrees of impact on waterlogging. Corresponding measures can be taken in urban flood management according to the identification of areas experiencing drainage difficulties.
