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Space-efficient algorithms for computing minimal/shortest unique substrings
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-09-14 , DOI: 10.1016/j.tcs.2020.09.017
Takuya Mieno , Dominik Köppl , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Given a string T of length n, a substring u=T[i..j] of T is called a shortest unique substring (SUS) for an interval [s,t] if (a) u occurs exactly once in T, (b) u contains the interval [s,t] (i.e. istj), and (c) every substring v of T with |v|<|u| containing [s,t] occurs at least twice in T. Given a query interval [s,t][1,n], the interval SUS problem is to output all the SUSs for the interval [s,t]. In this article, we propose a 4n+o(n) bits data structure answering an interval SUS query in output-sensitive O(occ) time, where occ is the number of returned SUSs. Additionally, we focus on the point SUS problem, which is the interval SUS problem for s=t. Here, we propose a (log23+1)n+o(n) bits data structure answering a point SUS query in the same output-sensitive time. We also propose space-efficient algorithms for computing the minimal unique substrings of T.



中文翻译:

空间高效的算法,用于计算最小/最短唯一子字符串

给定一个长度为n的字符串T,一个子字符串ü=Ť[一世Ĵ]T称为一定时间间隔内的最短唯一子串(SUS)[sŤ]如果(a)Ü发生正好一次在Ť,(B)Ü包含间隔[sŤ] (即 一世sŤĴ),以及(c)每子串vŤ|v|<|ü| 包含 [sŤ]T中至少发生两次。给定查询间隔[sŤ][1个ñ]间隔SUS问题是输出该间隔的所有SUS[sŤ]。在本文中,我们建议4ñ+Øñ 位数据结构在对输出敏感的情况下回答间隔SUS查询 ØØCC时间,其中OCC是返回SUSS的数量。另外,我们集中于点SUS问题,这是间隔SUS问题s=Ť。在这里,我们建议日志23+1个ñ+Øñ位数据结构在相同的输出敏感时间内回答一个点SUS查询。我们还提出了计算节省空间的算法最小的独特子牛逼

更新日期:2020-09-14
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