TY - GEN

T1 - Approximate Matching in the L1 Metric

AU - Amihood, A.

AU - Lipsky, O

AU - Porat, E

AU - Umanski, J

N1 - Place of conference:Jeju Island, Korea

PY - 2005

Y1 - 2005

N2 - 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 L 1 metric – the k- L 1 -distance problem. Given text T=t 0,...,t n − 1 and pattern P=p 0,...,p m − 1 strings of natural number, and a natural number k, we seek all text locations i where the L 1 distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. ∑m−1j=0|ti+j−pj|≤k∑j=0m−1|ti+j−pj|≤k.
We provide an algorithm that solves the k-L 1-distance problem in time O(nklogk−−−−−√)O(nklogk). The algorithm applies a bounded divide-and-conquer approach and makes novel uses of non-boolean convolutions.

AB - 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 L 1 metric – the k- L 1 -distance problem. Given text T=t 0,...,t n − 1 and pattern P=p 0,...,p m − 1 strings of natural number, and a natural number k, we seek all text locations i where the L 1 distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. ∑m−1j=0|ti+j−pj|≤k∑j=0m−1|ti+j−pj|≤k.
We provide an algorithm that solves the k-L 1-distance problem in time O(nklogk−−−−−√)O(nklogk). The algorithm applies a bounded divide-and-conquer approach and makes novel uses of non-boolean convolutions.

UR - https://scholar.google.co.il/scholar?q=Approximate+Matching+in+the+L1+Metric%2C+Amir+Amihood+&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - Annual Symposium on Combinatorial Pattern Matching

A2 - Apostolico, Alberto

A2 - Crochemore, Maxime

A2 - Park, Kunsoo

PB - Springer Berlin Heidelberg

ER -