All-pairs suffix/prefix in optimal time using Aho-Corasick space
The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S1,…,Sk} of k strings of total length n, we are asked to find, for each string Si, i∈[1,k], its longest suffix that is a prefix of string Sj, for all j≠i, j∈[1,k...
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| Published in: | Information processing letters Vol. 178; p. 106275 |
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01.11.2022
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| Abstract | The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S1,…,Sk} of k strings of total length n, we are asked to find, for each string Si, i∈[1,k], its longest suffix that is a prefix of string Sj, for all j≠i, j∈[1,k]. Several algorithms running in the optimal O(n+k2) time for solving APSP are known. All of these algorithms are based on suffix sorting and thus require space Ω(n) in any case. We consider the parameterized version of the APSP problem, denoted by ℓ-APSP, in which we are asked to output only the pairs whose suffix/prefix overlap is of length at least ℓ. We give an algorithm for solving ℓ-APSP that runs in the optimal O(n+|OUTPUTℓ|) time using O(n) space, where OUTPUTℓ is the set of output pairs. Our algorithm is thus optimal for the APSP problem as well by setting ℓ=0. Notably, our algorithm is fundamentally different from all optimal algorithms solving the APSP problem: it does not rely on sorting the suffixes of all input strings but on a novel traversal of the Aho-Corasick machine, and it thus requires space linear in the size of the machine.
•All-pairs suffix/prefix of length at least ℓ in optimal time.•All-pairs suffix/prefix in optimal time without suffix sorting.•All-pairs suffix/prefix in optimal time using Aho-Corasick space. |
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| AbstractList | The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S1,…,Sk} of k strings of total length n, we are asked to find, for each string Si, i∈[1,k], its longest suffix that is a prefix of string Sj, for all j≠i, j∈[1,k]. Several algorithms running in the optimal O(n+k2) time for solving APSP are known. All of these algorithms are based on suffix sorting and thus require space Ω(n) in any case. We consider the parameterized version of the APSP problem, denoted by ℓ-APSP, in which we are asked to output only the pairs whose suffix/prefix overlap is of length at least ℓ. We give an algorithm for solving ℓ-APSP that runs in the optimal O(n+|OUTPUTℓ|) time using O(n) space, where OUTPUTℓ is the set of output pairs. Our algorithm is thus optimal for the APSP problem as well by setting ℓ=0. Notably, our algorithm is fundamentally different from all optimal algorithms solving the APSP problem: it does not rely on sorting the suffixes of all input strings but on a novel traversal of the Aho-Corasick machine, and it thus requires space linear in the size of the machine.
•All-pairs suffix/prefix of length at least ℓ in optimal time.•All-pairs suffix/prefix in optimal time without suffix sorting.•All-pairs suffix/prefix in optimal time using Aho-Corasick space. The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S 1 ,. .. , S k } of k strings of total length n, we are asked to find, for each string S i , i ∈ [1, k], its longest suffix that is a prefix of string S j , for all j = i, j ∈ [1, k]. Several algorithms running in the optimal O(n + k 2) time for solving APSP are known. All of these algorithms are based on suffix sorting and thus require space (n) in any case. We consider the parameterized version of the APSP problem, denoted by-APSP, in which we are asked to output only the pairs whose suffix/prefix overlap is of length at least. We give an algorithm for solving-APSP that runs in the optimal O(n + |OUTPUT |) time using O(n) space, where OUTPUT is the set of output pairs. Our algorithm is thus optimal for the APSP problem as well by setting = 0. Notably, our algorithm is fundamentally different from all optimal algorithms solving the APSP problem: it does not rely on sorting the suffixes of all input strings but on a novel traversal of the Aho-Corasick machine, and it thus requires space linear in the size of the machine. |
| ArticleNumber | 106275 |
| Author | Pissis, Solon P. Loukides, Grigorios |
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| Cites_doi | 10.1016/j.ipl.2005.11.019 10.1186/1471-2105-13-82 10.1137/0222058 10.1016/0020-0190(92)90176-V 10.1016/j.ipl.2009.10.015 10.1145/360825.360855 10.1016/j.ipl.2019.105862 10.1007/BF01840391 10.1016/j.tcs.2017.07.013 10.1016/j.jda.2016.04.002 |
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| Keywords | String algorithms Data structures Failure transition tree Algorithms Aho-Corasick machine |
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| Snippet | The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S1,…,Sk} of k... The all-pairs suffix/prefix (APSP) problem is a classic problem in computer science with many applications in bioinformatics. Given a set {S 1 ,. .. , S k } of... |
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| SubjectTerms | Aho-Corasick machine Algorithms Computer Science Data structures Failure transition tree String algorithms |
| Title | All-pairs suffix/prefix in optimal time using Aho-Corasick space |
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