The Truth, the Whole Truth, and Nothing but the Truth: Alphabet Independent Two Dimensional Witness Table Construction

Abstract

The current explosion of stored information necessitates a new model of pattern matching, that of compressed matching. In this model one tries to find all occurrences of a pattern in a compressed text in time proportional to the compressed text size, i.e., without decompressing the text. The most effective general purpose compression algorithms are adaptive, in that the text represented by each compression symbol is determined dynamically by the data. As a result, the encoding of a substring depends on its location. Thus the same substring may “look different” every time it appears in the compressed text. In this paper we consider pattern matching without decompression in the UNIX Z-compression. This is a variant of the Lempel-Ziv adaptive compression scheme. If n is the length of the compressed text and m is the length of the pattern, our algorithms find the first pattern occurrence in time O (n +m ²) or O (n log m + m). We also introduce a new criterion to measure compressed matching algorithms, that of extra space. We show how to modify our algorithms to achieve a tradeoff between the amount of extra space used and the algorithm's time complexity.