Minimizing Setup and Beam-On Times in Radiation Therapy

摘要: Radiation therapy is one of the commonly used cancer therapies. The radiation treatment poses a tuning problem: it needs to be effective enough destroy tumor, but should maintain functionality organs close tumor. Towards this goal design has customized for each patient. Part are intensity matrices that define dosage in discretization beam head. To minimize time patient beam-on and setup need minimized. For given row matrix, minimum equivalent number binary vectors with consecutive “1”s property sum row, distinct set row. We give simple linear algorithm compute time. prove problem APX-hard approximation algorithms using duality property. general case, we $\frac {24}{13}$ algorithm. unimodal rows, 97$ also consider other variants which better ratios exist.