This algo doesn't fit for getter innerHTML/outerHTML in XML case:
http://www.w3.org/TR/DOM-Parsing/#dfn-concept-fragment-serializing-algorithm

If I correct then we have:

- for innerHTML algo try serializing passed context object, but should operate only on its childs (what we see in HTML fragment serialization algorithm: "This algorithm serializes the children of the node being serialized, not the node itself.")

http://www.w3.org/TR/DOM-Parsing/#widl-Element-innerHTML
"On getting, return the result of invoking the fragment serializing algorithm on the context object providing true for the require well-formed flag (this might throw an exception instead of returning a string)."

- for outerHTML you pass some "fictional node", but what is this (has namespace, has owner document?) and how the algorithm should handle it? This term is not too general, even for HTML fragment serialization algorithm (which accepts only Element, Document, or DocumentFragment)?