Concurrent Search and Insertion in K-Dimensional Height Balanced Trees

Abstract: K-Dimensional Height Balanced Trees represent one solution to handle simultaneous tree operations (insertion, search) with multiple value keys in an efficient way. The current paper focuses on discussing some of the intricacies and overhead caused by the concurrency aspects, as well as providing an implementation of the algorithm, together with a discussion regarding its correctness. 1. Context / Related work A fairly common way to organize information is in a hierarchical order. Trees, as a data structure, are a special kind of graph: a connected a-cyclic one. In order to efficiently perform operations on such a data structure (i.e. search, sort, insert, delete), the idea of binary search trees seemed as a valid option. Certain concerns related to the tree operations time complexity pioneered solutions like AVL-Trees, Red-Black Trees (a special type of AVL trees), B-Trees, in the attempt to optimize the time complexity of the tree operations. Multiple dimension height balanced trees are a more generalized type of AVL-tree. In such a data structure, all the basic tree operations (insertions, deletions, searches) can be performed in at most O(log n) time. K-Dimensional Height Balance