Pattern Matching by means of Multi-Resolution Compression

Introduction: The problem of compressed pattern matching deals with ways to find a pattern within a compressed file, without decompressing it first. The techniques for solving this problem fall into two major categories – creating a unique compression scheme that enables efficient pattern matching; or using some known compression scheme and develop algorithms to search the files it produces. In our work we have selected the first approach, trading off compression for fast pattern matching. Multi-resolution coding: In a multi-resolution coding scheme, a file is coded in several layers, where the first layer reveals only partial information about the file, and each layer adds information until the file is completely decoded. In order to implement such coding in text files, we divide the alphabet to non overlapping subgroups. The first encoded layer is a list of codes denoting the subgroup to which each symbol belong. The second encoded layer resolves the specific symbol within each subgroup (we used only two levels of resolution, but the method can be adopted to more levels). The problem of optimal subgroup division has previously been encountered in the as an optimization problem of the CodePack compression scheme, and has been previously addressed by the authors. Searching in multi-resolution encoded files: An important property of the coding method mentioned is that a string over the source alphabet is converted into a unique list of subsets. In the other direction the uniqueness property, of course, does not hold. Using this property the following algorithm is used: