Threshold Approximate Matching in Grammar-Compressed Strings

A grammar-compressed (GC) string is a string generated by a context-free grammar. This compression model captures many practical applications, and includes LZ78 and LZW compression as a special case. We give an efficient algorithm for threshold approximate matching on a GC-text against a plain pattern. Our algorithm improves on existing algorithms whenever the pattern is sufficiently long. The algorithm employs the technique of fast unit-Monge matrix distance multiplication, as well as a new technique for implicit unit-Monge matrix searching, which we believe to be of independent interest.