How do I manipulate a tree of immutable objects?

I'm building an entire application out of immutable objects so that multi-threading and undo become easier to implement. I'm using the Google Collections Library which provides immutable versions of Map, List, and Set.

My application model looks like a tree:

Scene is a top-level object that contains a reference to a root Node.
Each Node can contain child Nodes and Ports.

An object graph might look like this:

Scene
 |
 +-- Node
      |
      +-- Node 
           |
           +- Port
      +-- Node
           |
           +- Port
           +- Port

If all of these objects are immutable, controlled by a top-level SceneController object:

What is the best way to construct this hierarchy?
How would I replace an object that is arbitrarily deep in the object tree?
Is there a way to support back-links, e.g. a Node having a "parent" attribute?

And more generally:

Have any patterns emerged for dealing with this type of data?
Is there (academic) literature available on the subject?
Is this a good idea?

Solution

There are two concepts of interest here. First, persistent data structures. If all elements of the tree are immutable, then one can derive a new tree from the original tree by replacing some parts, but referring to the older parts, thus saving time and memory.

For example, if you were to add a third Port to the Node that has two ports already, you'd have to create a new Scene, a new Scene's Node's descendant, and the Node that you are changing. The other Node and all of the Ports do not need to be created anew -- you just refer to them in the new Scene/Nodes.

The other concept is that of a Zipper. A zipper is a way to "navigate" through a persistent data structure to optimize local changes. For instance, if you added four new Ports instead of just one, but you added each Port one at a time, you'd have to create four new Scenes, and eight new Nodes. With a zipper, you defer such creations until you are done, saving up on those intermediary objects.

The best explanation I ever read about zipper is here.

Now, use of a zipper to navigate a data structure remove the need to have back-links. You can have back-links in an immutable structure, by clever use of recursive constructors. However, such a data structure would not be persistent. Non-persistent immutable data structures have lousy modification performance, because you need to copy the whole data each time.

As for academic literature, I recommend Purely Function Data Structures, by Okasaki (dissertation PDF, fully fledged book).