How can simplify the octree in opencl kernel code?

Hi 
Thank you so much for share your code.
In your opencl kernel code, how to simplify the octree like your https://github.com/nickgildea/DualContouringSample or https://github.com/aewallin/dualcontouring ?
Actually I want to implement the simplification introduced in the original papaer(https://www.cse.wustl.edu/~taoju/research/dualContour.pdf).
Please give me some guideline.