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A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n, but the cost of search, insert, and delete operations grows with the depth of the tree. As with any balanced tree, the cost grows much more slowly than the number of elements.
Deletion from vEB trees is the trickiest of the operations. The call Delete(T, x) that deletes a value x from a vEB tree T operates as follows: If T.min = T.max = x then x is the only element stored in the tree and we set T.min = M and T.max = −1 to indicate that the tree is empty.
3.2 Set operations. 3.2.1 Contains key. 3.2.2 Set ... A trie is a type of search tree where – unlike for example a B-tree – keys are not stored in the nodes but ...
The white set, or condemned set, is the set of objects that are candidates for having their memory recycled. The black set is the set of objects that can be shown to have no outgoing references to objects in the white set, and to be reachable from the roots. Objects in the black set are not candidates for collection.
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
This operation is done to determine if the element is either in the list or in a 2–4 tree. A 2–4 tree is used when a delete operation occurs. If the item x is already in tree T, the item is removed using the 2–4 tree delete operation. Otherwise, the item x is in list L (done by checking if the bit variable is set). All the elements stored ...
When a second child is cut, the node itself needs to be cut from its parent and becomes the root of a new tree (see Proof of degree bounds, below). The number of trees is decreased in the operation delete-min, where trees are linked together. As a result of a relaxed structure, some operations can take a long time while others are done very ...
In theory, many other abstract data structures can be viewed as set structures with additional operations and/or additional axioms imposed on the standard operations. For example, an abstract heap can be viewed as a set structure with a min(S) operation that returns the element of smallest value.