How we can define Super-Greedy Linear extension of a Poset

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I am trying to understand the Super-Greedy linear extension of a poset. It is a topic of discrete mathematics, and I have tried to search the web, but only got one useful definition which I can't comprehend completely. I will attach the definition here, it would be a great help if anyone can help me to understand it: Supergreedy Algorithm.

If someone wants to dig into it, here is the complete paper.

Thanks in Advance