ReducedCBT and SuperCBT: two new and improved complete binary tree structures

Abstract

Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local hierarchy are introduced. The result of the first proposed hierarchy is a faster and smaller footprint, while the second one provides size variation functionality without a significant computational overhead. Complexity comparison between the algorithms based on the introduced local hierarchies and ones based on previous complete binary tree structures reveals that the novel approach brings considerable memory gains and performance boosts to the complete binary tree based algorithms.