Fast coupled path planning: From pseudo-polynomial to polynomial

Abstract

The coupled path planning (CPP) problem models the motion paths of the leaves of a multileaf collimator for optimally reproducing the prescribed dose in intensity-modulated radiation therapy (IMRT). Two versions of the CPP problem, unconstrained and constrained CPPs, are studied based on whether specifying the starting and ending positions of the leave paths. By exploring the underlying properties of the problem such as submodularity and L -convexity, we solve both CPP problems in polynomial time using the path-end hopping, local searching and proximity scaling techniques, improving current best known pseudo-polynomial time algorithms. Our algorithms are simple and easy to be implemented. Experimental results on real medical data showed that our CPP algorithms outperformed previous best-known algorithm by at least one order of magnitude. © 2010 Springer-Verlag Berlin Heidelberg.