Why is Perseus and Andromeda's relationship important to the story?

I think Persues and Andromeda's relationship was important to this story because unlike Thesues who betrayed Ariadne, Persues stayed loyal to Andromeda and did not betray her.

one thousand and one nights, also known as arabian nights is a collection of stories whose basic structure is that of embedded narrative. this technique refers to a main story which works as the common frame - or framing narrative - for the other stories, and then this series of stories which are connected to the main one. this technique can also be referred to as a story within a story. the stories stem from the original tale, some begin and end on their own, some are connected to the previous or following one, by means of questions that are answered in the subsequent tale, or characters which reappear.