getting correct meaning by analyzing a sentence

I have following paragraph and trying to understand what it clearly mention.

This paper shows several extensions and discusses the topology
approach, while recognizing that reconstruction of height jumps is a
challenge (A, 2010; B, 2007) and describing problems related to
intersection lines and jump edges between two segments.

first sentence is clear to me. I have problem with while part. It contains that also. So, I am confused. I want to know this and describing.. is related to that or while.

If I simplify my question,

Does the stricture of second part is

  1. while recognizing (X) and describing (Y) or..
  2. while recognizing that
    (P and describing Q).

UPDATE:
If I like to modify 1, Would it be possible to use one recognition as while recognizing (X) and (Y). I think yes, But Y is too long, Does this misguide the reader?

Can anyone help me to get the idea of this. thanks

Answer

The structure of the second part is:

  1. while recognizing (X) and describing (Y)

For clarity:

This paper shows several extensions and discusses the topology
approach, while (1) recognizing that reconstruction
of height jumps is a challenge (A, 2010; B, 2007), and (2) describing
problems related to intersection lines and jump edges between two segments.

EDIT: For your second question, I think you’re asking for this:

This paper shows several extensions and discusses the topology
approach, while recognizing that (1) reconstruction
of height jumps is a challenge (A, 2010; B, 2007), and that (2)
problems related to intersection lines and jump edges between two segments
are also challenges.

Note that in the above paragraph, I have added “are also challenges” to the end of (2) in order for the fragment to make some sense.

Attribution
Source : Link , Question Author : gnp , Answer Author : Chris Mukherjee

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