| Optimal resilient dynamic dictionaries (2007) | |||||||||||||||
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| Abstract. In the resilient memory model any memory cell can get corrupted at any time, and corrupted cells cannot be distinguished from uncorrupted cells. An upper bound, δ, on the number of corruptions and O(1) reliable memory cells are provided. In this model, a data structure is denoted resilient if it gives the correct output on the set of uncorrupted elements. We propose two optimal resilient static dictionaries, a randomized one and a deterministic one. The randomized dictionary supports searches in O(log n + δ) expected time using O(log δ) random bits in the worst case, under the assumption that corruptions are not performed by an adaptive adversary. The deterministic static dictionary supports searches in O(log n + δ) time in the worst case. We also introduce a deterministic dynamic resilient dictionary supporting searches in O(log n + δ) time in the worst case, which is optimal, and updates in O(log n + δ) amortized time. Our dynamic dictionary supports range queries in O(log n + δ + k) worst case time, where k is the size of the output. 1 | |||||||||||||||
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