Theoretical Computer Science
Text compression
Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
A New Linear-Time ``On-Line'' Algorithm for Finding the Smallest Initial Palindrome of a String
Journal of the ACM (JACM)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the 13th Australasian workshop on combinatorial algorithms
Algorithms on Strings
Succinct data structures for flexible text retrieval systems
Journal of Discrete Algorithms
Algorithmic Aspects of Bioinformatics (Natural Computing Series)
Algorithmic Aspects of Bioinformatics (Natural Computing Series)
Computing Longest Previous Factor in linear time and applications
Information Processing Letters
A Simple Algorithm for Computing the Lempel Ziv Factorization
DCC '08 Proceedings of the Data Compression Conference
Searching for Gapped Palindromes
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Linear Time Suffix Array Construction Using D-Critical Substrings
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Combinatorial Algorithms
Linear-time construction of suffix arrays
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Space efficient linear time construction of suffix arrays
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Simple linear work suffix array construction
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Theoretical and practical improvements on the RMQ-Problem, with applications to LCA and LCE
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
A new succinct representation of RMQ-information and improvements in the enhanced suffix array
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Variations of the parameterized longest previous factor
Journal of Discrete Algorithms
On parsing optimality for dictionary-based text compression-the Zip case
Journal of Discrete Algorithms
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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The concept of a longest previous factor (LPF) is inherent to Ziv-Lempel factorization of strings in text compression, as well as in statistics of repetitions and symmetries. It is expressed in the form of a table - LPF[i] is the maximum length of a factor starting at position i, that also appears earlier in the given text. We show how to compute efficiently three new tables storing different variants of previous factors (past segments) of a string. The longest previous non-overlapping factor, for a given position i, is the longest factor starting at i which has an exact copy occurring entirely before, while the longest previous non-overlapping reverse factor for a given position i is the longest factor starting at i, such that its reverse copy occurs entirely before. In both problems the previous copies of the factors are required to occur within the prefix ending at position i-1. The longest previous (possibly overlapping) reverse factor is the longest factor starting at i, such that its reverse copy starts before i. These problems have not been explicitly considered before, but they have several applications and they are natural extensions of the longest previous factor problem, which has been extensively studied. Moreover, the newly introduced tables store additional information on the structure of the string, helpful to improve, for example, gapped palindrome detection and text compression using reverse factors.