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 inplace. We analytically determine the complexity of our algorithms and empirically measure their performance. Results indicate that on both CPU and GPU architectures B-tree layouts provide the best query performance. However, when considering the total time to permute the data and to perform a series of search queries, our vEB permutation provides the best performance on the CPU. We show that, given an input of N=500M 64-bit integers, the benefits of query performance (compared to binary search) outweigh the cost of in-place permutation using our algorithms when performing at least 5M queries (1% of N) and 27M queries (6% of N), on our CPU and GPU platforms, respectively.