Refined Buneman Trees

interface EdgeIterator
{
boolean hasNext();
}
Edge next();
Figure 6.5: The interface for the EdgeIterator class
6.2 Operations on the tree datastructure
The tree datastructure maintains a compatible set of splits. And the operations
we are interested in supporting are the following:
• Insert(σ)
Of course, we need to be able to insert splits into our set of splits
• Delete(σ)
And we need to be able to remove splits from the set
• Incompatible(σ)
And finally we need to be able to determine if a split is compatible with
any split in our compatible set of splits, and if there is one, to extract it.
The following sections describe in detail how these operations have been
implemented. In order to support the operations on the tree data structure
needed in the refined Buneman algorithm, we must be able to search through
the tree, and find both nodes and edges.
For the insert operation we will need to locate a node with the property that
for a split σ = U|V the node seperates U and V in the sense that we can group
its subtrees in two, where one group only contains elements from U, andthe
other group only contains elements from V . This node can then be expanded
into two connected nodes, one for each subtree group.
For the delete operation we need to be able to find the edge e that seperates U
and V , meaning that the node on one of the edge is root in a subtree containing
only elements from U, and the node on the other end is root in a subtree
containiing only elements from V .
For the incompatible operation we need to be able to find en edge e which
is incompatible with another edge e ′ . We will use Definition 3 to decide the
question of incompatibility.
6.2.1 Insert
Assume we have an unrooted tree T , and that we have selected some random
node w root as starting point for traversal. The task is to insert a split σ = U|V
which is compatible with all other splits represented by T . This amounts to
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