Adapting the Knuth–Morris–Pratt algorithm for pattern matching in Huffman encoded texts

Abstract

In the present work we perform compressed pattern matching in binary Huffman encoded texts [Huffman, D. (1952). A method for the construction of minimum redundancy codes, Proc. of the IRE, 40, 1098-1101]. A modified Knuth-Morris-Pratt algorithm is used in order to overcome the problem of false matches, i.e., an occurrence of the encoded pattern in the encoded text that does not correspond to an occurrence of the pattern itself in the original text. We propose a bitwise KMP algorithm that can move one extra bit in the case of a mismatch since the alphabet is binary. To avoid processing any bit of the encoded text more than once, a preprocessed table is used to determine how far to back up when a mismatch is detected, and is defined so that we are always able to align the start of the encoded pattern with the start of a codeword in the encoded text. We combine our KMP algorithm with two practical Huffman decoding schemes which handle more than a single bit per machine operation; skeleton trees defined by Klein [Klein, S. T. (2000). Skeleton trees for efficient decoding of huffman encoded texts. Information Retrieval, 3, 7-23], and numerical comparisons between special canonical values and portions of a sliding window presented in Moffat and Turpin [Moffat, A., & Turpin, A. (1997). On the implementation of minimum redundancy prefix codes. IEEE Transactions on Communications, 45, 1200-1207]. Experiments show rapid times of our algorithms compared to the decompress then search method, therefore, files can be kept in their compressed form, saving memory space. When compression gain is important, these algorithms are better than cgrep [Ferragina, P., Tommasi, A., & Manzini, G. (2004). C Library to over compressed texts, http://roquefort.di.unipi.it/~ferrax/CompressedSearch], which is only slightly faster than ours.