Range LCP Queries Revisited
Range LCP Queries Revisited
复制标题
重新审视范围 LCP 查询
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Sharma V. Thankachan
中科院分区：
文献类型：
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作者：
A. Amir;Moshe Lewenstein;Sharma V. Thankachan
范围LCP问题是预处理一个字符串$$ s [1dots n] $$，以启用以下查询的有效解决方案：给定一个范围[l，ixi¾r]作为输入，报告$$ max _ {i，j in {l，ldots，r}} | Mathsf {lcp} s_ {i}，s_j | $$。 J和$$ | MATHSF {LCP} S_I，S_J | $$是我们的长度。 $$ MATHSF {LCP} $$计算中的不匹配。 ：$$ max _ {{{ell _1le ile r_1，ell _2le jle jle r_2}} | mathsf {lcp} _ks_i，s_j | $ $ $ $ $$ MATHSF {lcp} _ks_i，s_j $ j $ $和$$ s_j $$最多可以使用k n $$在^2/w $$空间数据结构上回答问题$$ k = 0 $$和$$ k = 1 $$的空间有效数据结构。 {epsilon} n $$，其中w是单词大小和$$ epsilon> 0 $$是任意小的常数。
对于情况，$$ k = 1 $$，我们获得了一个$$ onlog n $$空间数据结构，带有查询时间$$ osqrt {n} log n $$。
最后，我们从设定的交叉点减少到范围LCP查询，这表明将我们的上限提高超过$$ og of ^{epsilon} n $$的限制将非常困难。
The Range LCP problem is to preprocess a string $$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$$.