Can anyone explain the water filling algorithm in the easiest way?

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Can anyone explain the water filling algorithm in the easiest way?

Because i saw some paper which use the water filling algorithm to find the optimal solution,and i still don't understand what is water filling

why is it called water filling?because after i saw the step of water filling,i still don't understand why is it called water filling

What method does it actually do?like using bisection or differential?

what is its concept?

paper link:https://www.semanticscholar.org/paper/Water-Filling%3A-A-Geometric-Approach-and-its-to-He-Zhao/ae1d179a55c0cc12752002c4ffba92211405ac2d

https://ieeexplore.ieee.org/document/6583145