Then the cost of performing on a splay tree is .

This complicates the use of such splay trees in a multi-threaded environment.

A simple amortized analysis of static splay trees can be carried out using the potential method.

It should not be confused with a finger tree nor a splay tree.

This is in contrast to splay trees which have a worst-case time of O(n).

Then the cost for a splay tree to perform the same accesses is .

A splay tree can be worse than a static tree by at most a constant factor.

This implementation is based on the first method of deletion on a splay tree.

Therefore, offering an alternative to splay trees.

The texture underpaw changed to groomed hook-turf between splayed tree roots.

To insert a node x into a splay tree:

Below there is an implementation of splay trees in C++, which uses pointers to represent each node on the tree.

Traversal Conjecture: Let and be two splay trees containing the same elements.

Splay trees can change even when they are accessed in a 'read-only' manner (i.e. by find operations).

Split Conjecture: Let be any permutation of the elements of the splay tree.

Several general-purpose priority queue algorithms have proven effective for discrete-event simulation, most notably, the splay tree.

It may also be used to analyze splay trees, a self-adjusting form of binary search tree with logarithmic amortized time per operation.

In related work, Jones applied splay trees to data compression and developed algorithms for applying parallel computing to discrete event simulation.

A splay tree is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again.

Splay trees are self adjusting search trees introduced by Sleator and Tarjan in 1985.

Using restructuring heuristic, splay trees are able to achieve insert and delete operations in amortized time, without storing any balance information at the nodes.

For many sequences of non-random operations, splay trees perform better than other search trees, even when the specific pattern of the sequence is unknown.

Then the potential function P(t) for a splay tree t is the sum of the ranks of all the nodes in the tree.

In other words, splay trees perform as well as static balanced binary search trees on sequences of at least n accesses.

In addition to the proven performance guarantees for splay trees there is an unproven conjecture of great interest from the original Sleator and Tarjan paper.