In this paper we have developed an algorithm that converts a given k-ary tree, for any k ≥ 3, to its equivalent binary tree structure. The binary tree is generated in O(n) time, for a k-ary tree with a total of n nodes. The algorithm is designed aiming at reducing the height of the constructed binary tree. The constructed tree does not contain any free links in the non-leaf nodes. That means th...

Tree-like hierarchical structure is one of the key features in many real complex systems. To investigate its properties, a deterministic tree-like hierarchical network model is proposed. Next, the static properties of the tree-like hierarchical networks are discussed. The simulation and theoretical results prove that the artificial tree-like networks conformably possess small-world and scalefre...

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence—any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any othe...