Near-Optimal Search Time in δ-Optimal Space
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Two recent lower bounds on the compressiblity of repetitive sequences, δ≤γ, have received much attention. It has been shown that a string S[1..n] can be represented within the optimal O(δlogn/δ) space, and further, that within that space one can find all the occ occurrences in S of any pattern of length m in time O(mlog n + occ log^ϵ n) for any constant ϵ>0. Instead, the near-optimal search time O(m+(occ+1)log^ϵ n) was achieved only within O(γlogn/γ) space. Both results are based on considerably different locally consistent parsing techniques. The question of whether the better search time could be obtained within the δ-optimal space was open. In this paper we prove that both techniques can indeed be combined in order to obtain the best of both worlds, O(m+(occ+1)log^ϵ n) search time within O(δlogn/δ) space.
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