The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Efficient and secure generalized pattern matching via fast fourier transform
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
String matching with mismatches by real-valued FFT
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
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The string matching with mismatches problem requires finding the Hamming distance between a pattern P of length m and every length m substring of text T with length n. Fischer and Paterson's FFT-based algorithm solves the problem without error in O(@snlogm), where @s is the size of the alphabet @S [SIAM-AMS Proc. 7 (1973) 113-125]. However, this in the worst case reduces to O(nmlogm). Atallah, Chyzak and Dumas used the idea of randomly mapping the letters of the alphabet to complex roots of unity to estimate the score vector in time O(nlogm) [Algorithmica 29 (2001) 468-486]. We show that the algorithm's score variance can be substantially lowered by using a bijective mapping, and specifically to zero in the case of binary and ternary alphabets. This result is extended via alphabet remappings to deterministically solve the string matching with mismatches problem with a constant factor of 2 improvement over Fischer-Paterson's method.