On Performance Deviation of Binary Search Tree Searches from the Optimal Search Tree Search Structures

Binary Search Trees are a frequently used data structure for rapid access to the stored data. Data structures like arrays, vectors and linked lists are limited by the trade-off between the ability to perform a fast search and resize easily. They are an alternative that is both dynamic in size and easily searchable. Due to efficiency reason, complete and nearly complete binary search trees are of particular significance. This paper addresses the performance analysis and measurement, collectively known as the Performance in binary search tree search applications. Performance measurement is equally significant asides from the performance analysis to learn more about the deviation from optimality. To estimate this deviation, new performance criteria for the binary search trees are presented. A multi-key search algorithm is proposed and the related analysis followed. The algorithm is capable of searching for multiple key elements in the same execution, sacrificing some optimality in the timing consideration. This helps in pruning a subtree structure out of a given binary search tree for further processing. Keywords— Complete Binary Search Tree, Nearly Complete Binary Search Tree, Performance Criteria, Sparsity Factor, Density Factor, Multi-Key Search, Search-tree Pruning.