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...

Full description

Saved in:
Bibliographic Details
Published in:Information processing letters Vol. 178; p. 106275
Main Authors: Loukides, Grigorios, Pissis, Solon P.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2022
Elsevier
Subjects:
Aho-Corasick machine
Algorithms
Computer Science
Data structures
Failure transition tree
String algorithms
String algorithms
Data structures
Failure transition tree
Algorithms
Aho-Corasick machine
ISSN:0020-0190, 1872-6119
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2022.106275