The approach depends on the TreeModel used to construct your OutlineModel. In the FileTreeModel cited, getRoot() returns an arbitrary File representing the root of a subtree in a hierarchical file system. This subtree can be searched recursively as shown here. Instead of printing the results, you would accumulate the File instances representing the path into an array. That array would be used to construct a TreePath. Given such a treePath, you can reveal the corresponding node in a manner analogous to that shown here.
outline.expandPath(treePath);
outline.scrollRectToVisible(getPathBounds(treePath));