Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Algorithms for approximate string matching
Information and Control
Introducing efficient parallelism into approximate string matching and a new serial algorithm
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Fast parallel and serial approximate string matching
Journal of Algorithms
Recursive star-tree parallel data structure
SIAM Journal on Computing
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
A guided tour to approximate string matching
ACM Computing Surveys (CSUR)
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
Linear time algorithms for finding and representing all the tandem repeats in a string
Journal of Computer and System Sciences
Linear Time Suffix Array Construction Using D-Critical Substrings
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Practical Algorithms for the Longest Common Extension Problem
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
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
Longest common extensions via fingerprinting
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
ADCONS'11 Proceedings of the 2011 international conference on Advanced Computing, Networking and Security
Time-Space trade-offs for longest common extensions
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Time-space trade-offs for longest common extensions
Journal of Discrete Algorithms
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The Longest Common Extension (LCE) problem considers a string s and computes, for each pair (i,j), the longest substring of s that starts at both i and j. It appears as a subproblem in many fundamental string problems and can be solved by linear-time preprocessing of the string that allows (worst-case) constant-time computation for each pair. The two known approaches use powerful algorithms: either constant-time computation of the Lowest Common Ancestor in trees or constant-time computation of Range Minimum Queries in arrays. We show here that, from practical point of view, such complicated approaches are not needed. We give two very simple algorithms for this problem that require no preprocessing. The first is 5 times faster than the best previous algorithms on the average whereas the second is faster on virtually all inputs. As an application, we modify the Landau-Vishkin algorithm for approximate matching to use our simplest LCE algorithm. The obtained algorithm is 13 to 20 times faster than the original. We compare it with the more widely used Ukkonen's cutoff algorithm and show that it behaves better for a significant range of error thresholds.