A Boyer-Moore Type Algorithm for Compressed Pattern Matching

We apply the Boyer–Moore technique to compressed pattern matching for text string described in terms of collage system, which is a formal framework that captures various dictionary-based compression methods. For a subclass of collage systems that contain no truncation, our new algorithm runs in O(‖D‖ + n · m + m + r) time using O(‖D‖ + m) space, where ‖D‖ is the size of dictionary D, n is the compressed text length, m is the pattern length, and r is the number of pattern occurrences. For a general collage system, the time complexity is O(height(D)·(‖D‖+n)+n·m+m2+r), where height(D) is the maximum dependency of tokens in D. We showed that the algorithm specialized for the so-called byte pair encoding (BPE) is very fast in practice. In fact it runs about 1.2 ∼ 3.0 times faster than the exact match routine of the software package agrep, known as the fastest pattern matching tool.