SIAM Journal on Computing
Introduction to algorithms
Fast algorithms for approximately counting mismatches
Information Processing Letters
Alphabet dependence in parameterized matching
Information Processing Letters
Fast subsequence matching in time-series databases
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
Efficient 2-dimensional approximate matching of half-rectangular figures
Information and Computation
String matching under a general matching relation
Information and Computation
Fast time-series searching with scaling and shifting
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Verifying candidate matches in sparse and wildcard matching
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Identifying Representative Trends in Massive Time Series Data Sets Using Sketches
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximate matching in the L1 metric
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
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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Given an alphabet Σ ={1,2,...,|Σ |} text string T εΣ n and a pattern stringP ε Σ m , foreach i = 1,2,...,n - m + 1 defineL d (i ) as the d-normdistance when the pattern is aligned below the text and starts atposition i of the text. The problem of pattern matchingwith L p distance is to computeL p (i ) for every i = 1,2,...,n - m + 1. We discuss the problem ford = 1, ∞. First, in the case of L 1 matching (pattern matching with an L 1 distance) we present an algorithm that approximatesthe L 1 matching up to a factor of 1 +ε , which has an $O(\frac{1}{\varepsilon^2} n\logmlog |\Sigma|)$ run time. Second, we provide an algorithm thatapproximates the L ∞ matching up to afactor of 1 + ε with a run time of$O(\frac{1}{\varepsilon} n\log mlog |\Sigma|)$. We also generalizethe problem of String Matching with mismatches to have weightedmismatches and present an O (n log4m ) algorithm that approximates the results of this problemup to a factor of O (logm ) in the case that theweight function is a metric.