Faster Sparse Suffix Sorting

The sparse suffix sorting problem is to sort b = o(n) arbitrary suffixes of a string of length n using o(n) words of space in addition to the string. We present an O(n) time Monte Carlo algorithm using O(b log b) space and an O(n log b) time Las Vegas algorithm using O(b) space. This is a significant improvement over the best prior solutions by Bille et al. (ICALP 2013): a Monte Carlo algorithm running in O(n log b) time and O(b(1+epsilon)) space or O(n log 2 b) time and O(b) space, and a Las Vegas algorithm running in O(n log(2) b + b(2) log b) time and O(b) space. All the above results are obtained with high probability not just in expectation.