Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

We present parallel algorithms to efficiently permute a sorted array into the level-order binary search tree (BST), level-order B-tree (B-tree), and van Emde Boas (vEB) layouts in-place. We analytically determine the complexity of our algorithms and empirically measure their performance. When considering the total time to permute the data in-place and to perform a series of search queries, the vEB layout provides the best performance on the CPU. Given an input of $N$N=537 million 64-bit integers, the benefits of query performance (compared to binary search) outweigh the cost of in-place permutation when performing as few as 0.37% of $N$N queries. On the GPU, results depend on the particular architecture, with the B-tree and vEB layouts performing the best. The number of queries necessary to reach the break-even point with binary search ranges from 1.3% to 8.9% of $N$N=1,074 million 32-bit integers.