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- W2407628792 abstract "The Range LCP problem is to preprocess a string $$S[1dots n]$$, to enable efficient solutions of the following query: given a range [l,i¾źr] as the input, report $$max _{i, j in {l,ldots ,r}} |mathsf {LCP}S_{i}, S_j|$$. Here $$mathsf {LCP}S_i, S_j$$ is the longest common prefix of the suffixes of S starting at locations i and j and $$|mathsf {LCP}S_i,S_j|$$ is its length. We study a natural extension of this problem, where the query consists of two ranges. Additionally, we allow a bounded number say $$kge 0$$ of mismatches in the $$mathsf {LCP}$$ computation. Specifically, our task is to report the following when two ranges $$[ell _1, r_1]$$ and $$[ell _2,r_2]$$ comes as input: $$max _{{ell _1le ile r_1, ell _2le jle r_2}}|mathsf {LCP}_kS_i,S_j|$$Here $$mathsf {LCP}_kS_i,S_j$$ is the longest prefix of $$S_i$$ and $$S_j$$ with at most k mismatches allowed. We show that the queries can be answered in Ok time using an $$On^2/w$$ space data structure, where w is the word size. We also present space efficient data structures for $$k=0$$ and $$k=1$$. For $$k=0$$, we obtain a linear space data structure with query time $$Osqrt{n/w}log ^{epsilon } n$$, where w is the word size and $$epsilon >0$$ is an arbitrarily small constant.For the case $$k=1$$ we obtain an $$Onlog n$$ space data structure with query time $$Osqrt{n}log n$$.Finally, we give a reduction from Set Intersection to Range LCP queries, suggesting that it will be very difficult to improve our upper bound by more than a factor of $$Olog ^{epsilon }n$$." @default.
- W2407628792 created "2016-06-24" @default.
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- W2407628792 date "2015-01-01" @default.
- W2407628792 modified "2023-10-18" @default.
- W2407628792 title "Range LCP Queries Revisited" @default.
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- W2407628792 doi "https://doi.org/10.1007/978-3-319-23826-5_33" @default.
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