TY - GEN

T1 - Approximated Pattern Matching with the l 1, l 2 and l∞ Metrics

AU - Lipsky, Ohad

AU - Porat, E.

N1 - Place of conference:Australia

PY - 2008

Y1 - 2008

N2 - Given an alphabet Σ = {1,2,...,|Σ|} text string T ∈ Σ n and a pattern string P ∈ Σ m , for each i = 1,2,...,n − m + 1 define L d (i) as the d-norm distance when the pattern is aligned below the text and starts at position i of the text. The problem of pattern matching with L p distance is to compute L p (i) for every i = 1,2,...,n − m + 1. We discuss the problem for d = 1, ∞. First, in the case of L 1 matching (pattern matching with an L 1 distance) we present an algorithm that approximates the L 1 matching up to a factor of 1 + ε, which has an O(1ε2nlogmlog|Σ|)O(1ε2nlogmlog|Σ|) run time. Second, we provide an algorithm that approximates the L ∞ matching up to a factor of 1 + ε with a run time of O(1εnlogmlog|Σ|)O(1εnlogmlog|Σ|). We also generalize the problem of String Matching with mismatches to have weighted mismatches and present an O(nlog4 m) algorithm that approximates the results of this problem up to a factor of O(logm) in the case that the weight function is a metric.

AB - Given an alphabet Σ = {1,2,...,|Σ|} text string T ∈ Σ n and a pattern string P ∈ Σ m , for each i = 1,2,...,n − m + 1 define L d (i) as the d-norm distance when the pattern is aligned below the text and starts at position i of the text. The problem of pattern matching with L p distance is to compute L p (i) for every i = 1,2,...,n − m + 1. We discuss the problem for d = 1, ∞. First, in the case of L 1 matching (pattern matching with an L 1 distance) we present an algorithm that approximates the L 1 matching up to a factor of 1 + ε, which has an O(1ε2nlogmlog|Σ|)O(1ε2nlogmlog|Σ|) run time. Second, we provide an algorithm that approximates the L ∞ matching up to a factor of 1 + ε with a run time of O(1εnlogmlog|Σ|)O(1εnlogmlog|Σ|). We also generalize the problem of String Matching with mismatches to have weighted mismatches and present an O(nlog4 m) algorithm that approximates the results of this problem up to a factor of O(logm) in the case that the weight function is a metric.

UR - https://scholar.google.co.il/scholar?q=Ohad+Lipsky%2C+Ely+Porat%3A+Approximated+Pattern+Matching+with+the+L1%2C+L2+and+Linfinit+Metrics&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - International Symposium on String Processing and Information Retrieval

A2 - Amir, Amihood

A2 - Turpin, Andrew

A2 - Moffat, Alistair

PB - Springer Berlin Heidelberg

ER -