Oblivious tight compaction in O(n) time with smaller constant

Oblivious compaction is a crucial building block for hash-based oblivious RAM. Asharov et al. recently gave a O(n) algorithm for oblivious tight compaction. Their algorithm is deterministic and asymptotically optimal, but it is not practical to implement because the implied constant is 2. We give a new algorithm for oblivious tight compaction that runs in time < 16014.54n. As part of our construction, we give a new result in the bootstrap percolation of random regular graphs.

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