I have a scenario where the IDs are unique but can have multiple Parents.

how is that possible?

media
...books
  ...fiction
      ...comedy
      ...mystery
  ...nonfiction
      ...history
      ...science
...cds
  ...music
  ...audio-books
      ...fiction
        ...comedy
        ...mystery
      ...non-fiction
        ...history
        ...science
...dvds
  ...narrative
      ...comedy
      ...mystery
  ...documentary
      ...history
      ...science