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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=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 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=1,074 million 32-bit integers.

Digital volume correlation (DVC) is a powerful and widely used technique for measuring the internal 3D deformation field of a wide range of materials. One of the most popular DVC algorithms is the reliability-guided DVC (RG-DVC) which is good at dealing with large continuous deformation. However, RG-DVC requires a manually specified seed from which computation starts, and suffers from the efficiency due to a huge amount of computation and data dependency. This paper proposes a GPU accelerated parallel reliability-guided DVC algorithm (CuSIFT-RGDVC) on CUDA, which leverages 3D scale-invariant feature transform (3D SIFT) to assist seed selection to realize fully automation and improves performance utilizing GPU computing. In CuSIFT-RGDVC, reliability-guided displacement tracking (RGDT) is rewritten using sorted array-based batch processing mechanism which is a globally sequential locally parallel model, and multi-granularity parallelism is adopted to maximize GPU utilization. The empirical result shows that the proposed CuSIFT-RGDVC provides up to 29.1x speedup compared with our multi-threaded implementation and achieves the same level of computation speed as the state-of-the-art path-independent DVC without sacrificing accuracy.