Near-Optimal Search Time in δ -Optimal Space

Abstract

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(δlognδ) 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+ occlog ϵn) for any constant ϵ> 0. Instead, the near-optimal search time O(m+ (occ+ 1 ) log ϵn) was achieved only within O(γlognγ) 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 ϵn) search time within O(δlognδ) space.