TY - GEN
T1 - Approximate matching in the L 1 metric
AU - Amihood, A.
AU - Lipsky, O
AU - Porat, E
AU - Umanski, J
N1 - Place of conference: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+Amihood+Amir%2C+Ohad+Lipsky%2C+Ely+Porat%2C+Julia+Umanski&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 -