Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Improved string matching with k mismatches
ACM SIGACT News
Efficient string matching with k mismatches
Theoretical Computer Science
SIAM Journal on Computing
Highly parallelizable problems
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Fast algorithms for approximately counting mismatches
Information Processing Letters
Efficient 2-dimensional approximate matching of half-rectangular figures
Information and Computation
A Space-Economical Suffix Tree Construction Algorithm
Journal of the ACM (JACM)
Verifying candidate matches in sparse and wildcard matching
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Linear pattern matching algorithms
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
Function matching: algorithms, applications, and a lower bound
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
All maximal-pairs in step-leap representation of melodic sequence
Information Sciences: an International Journal
Approximate matching in the L∞ metric
Information Processing Letters
L1 pattern matching lower bound
Information Processing Letters
A Black Box for Online Approximate Pattern Matching
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Approximated Pattern Matching with the L1 , L2 and L∞ Metrics
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
δ γ --- Parameterized Matching
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
A black box for online approximate pattern matching
Information and Computation
Faster algorithms for δ,γ-matching and related problems
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
L1 pattern matching lower bound
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
Approximate matching in the L∞ metric
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
European Journal of Combinatorics
Self-normalised distance with don't cares
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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Approximate matching is one of the fundamental problems in pattern matching, and a ubiquitous problem in real applications. The Hamming distance is a simple and well studied example of approximate matching, motivated by typing, or noisy channels. Biological and image processing applications assign a different value to mismatches of different symbols. We consider the problem of approximate matching in the L1 metric – the k-L1-distance problem. Given text T=t0,...,tn−1 and pattern P=p0,...,pm−1 strings of natural number, and a natural number k, we seek all text locations i where the L1 distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. $\sum_{j=0}^{m-1} |{t}_{i+j} - {p}_{j}| \leq k$. We provide an algorithm that solves the k-L1-distance problem in time $O(n\sqrt{k\log k})$. The algorithm applies a bounded divide-and-conquer approach and makes novel uses of non-boolean convolutions.