Before revision:  In contrast to the fast marching method and the fast sweeping method for the Eikonal equation, our improved method does not need to compute the solution with any special ordering in either the remedy list or the active list so that it can be implemented in parallel.
After revision:  In contrast to the fast marching method and the fast sweeping method for the Eikonal equation, our improved method does not need to compute the solution with any special ordering in either the remedy list or the active list . Therefore, our algorithm can be implemented in parallel.