The Boyer Moore Galil string searching strategies revisited
SIAM Journal on Computing
Theoretical Computer Science
Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Tight bounds on the complexity of the Apostolico-Giancarlo algorithm
Information Processing Letters
A fast string searching algorithm
Communications of the ACM
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithms on Strings
Computing Longest Previous Factor in linear time and applications
Information Processing Letters
Verifying a parameterized border array in O(n1.5) time
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Cover array string reconstruction
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Validating the knuth-morris-pratt failure function, fast and online
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Verifying and enumerating parameterized border arrays
Theoretical Computer Science
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The Longest Previous Factor (LPF) table of a string s of length n is a table of size n whose ith element indicates the length of the longest substring of s starting from position i that has appeared previously in s. LPF tables facilitate the computing of the Lempel-Ziv factorization of strings [21,22] which plays an important role in text compression. An open question from Clément, Crochemore and Rindone [4] asked whether the following problem (which we call the reverse LPF problem) can be solved efficiently: Given a table W, decide whether it is the LPF table of some string, and find such a string if so. In this paper, we address this open question by proving that the reverse LPF problem is NP-hard. Thus, there is no polynomial time algorithm for solving it unless P = NP. Complementing with this general hardness result, we also design a linear-time online algorithm for the reverse LPF problem over input tables whose elements are all 0 or 1.