Computer Science – Data Structures and Algorithms
Scientific paper
2009-09-05
Computer Science
Data Structures and Algorithms
Version of paper accepted to 2010 ACM-SIAM Symposium on Discrete Algorithms (SODA)
Scientific paper
In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high probability. Thus, randomized Shellsort is simultaneously simple, time-optimal, and data-oblivious. Taken together, these properties imply applications in the design of new efficient privacy-preserving computations based on the secure multi-party computation (SMC) paradigm. In addition, by a trivial conversion of this Monte Carlo algorithm to its Las Vegas equivalent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability.
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