Faster algorithms for string matching with k mismatches
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the shared substring alignment problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A guided tour to approximate string matching
ACM Computing Surveys (CSUR)
A sub-quadratic sequence alignment algorithm for unrestricted cost matrices
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Information Processing Letters
Combining Appearance and Topology for Wide Baseline Matching
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Approximate String Matching in LDAP Based on Edit Distance
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Algorithms for Local Alignment with Length Constraints
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
The Max-Shift Algorithm for Approximate String Matching
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Approximate Periods of Strings
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Information and Computation
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Longest common subsequence problem for unoriented and cyclic strings
Theoretical Computer Science
Discrete Applied Mathematics - 12th annual symposium on combinatorial pattern matching (CPM)
Two algorithms for LCS Consecutive Suffix Alignment
Journal of Computer and System Sciences
Semi-local longest common subsequences in subquadratic time
Journal of Discrete Algorithms
Indexed Hierarchical Approximate String Matching
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Finding All Approximate Gapped Palindromes
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Dynamic Edit Distance Table under a General Weighted Cost Function
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Discrete Applied Mathematics
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
New algorithms for efficient parallel string comparison
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Pseudo-realtime pattern matching: closing the gap
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Multiplication algorithms for Monge matrices
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Pattern matching in pseudo real-time
Journal of Discrete Algorithms
Approximate regular expression matching with multi-strings
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
All semi-local longest common subsequences in subquadratic time
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
On the complexity of sparse exon assembly
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Monge properties of sequence alignment
Theoretical Computer Science
Fully incremental LCS computation
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A parallel algorithm for fixed-length approximate string-matching with k-mismatches
Algorithms and Applications
Least random suffix/prefix matches in output-sensitive time
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Time-Space trade-offs for longest common extensions
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Efficient communication protocols for deciding edit distance
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Approximate regular expression matching with multi-strings
Journal of Discrete Algorithms
Sequential pattern mining -- approaches and algorithms
ACM Computing Surveys (CSUR)
Time-space trade-offs for longest common extensions
Journal of Discrete Algorithms
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The problem of comparing two sequences A and B to determine their longest common subsequence (LCS) or the edit distance between them has been much studied. In this paper we consider the following incremental version of these problems: given an appropriate encoding of a comparison between A and B, can one incrementally compute the answer for A and bB, and the answer for A and Bb with equal efficiency, where b is an additional symbol? Our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such "adjacent" problems. Given a threshold k on the number of differences to be permitted in an alignment, the theorem leads directly to an O(k) algorithm for incrementally computing a new solution from an old one, as contrasts the O(k2) time required to compute a solution from scratch. We further show, with a series of applications, that this algorithm is indeed more powerful than its nonincremental counterpart. We show this by solving the applications with greater asymptotic efficiency than heretofore possible. For example, we obtain O(nk) algorithms for the longest prefix approximate match problem, the approximate overlap problem, and cyclic string comparison.