Re-Pair is a grammar compression scheme with favorably good compression rates. The computation of Re-Pair comes with the cost of maintaining large frequency tables, which makes it hard to compute Re-Pair on large scale data sets. As a solution for this problem we present, given a text of length @math whose characters are drawn from an integer alphabet, an @math time algorithm computing Re-Pair in @math bits of space including the text space, where @math is the number of terminals and non-terminals. The algorithm works in the restore model, supporting the recovery of the original input in the time for the Re-Pair computation with @math additional bits of working space. We give variants of our solution working in parallel or in the external memory model.
The compression is an important topic in computer science which allows we to storage more amount of data on our data storage. There are several techniques to compress any file. In this manuscript will be described the most important algorithm to compress images such as JPEG and it will be compared with another method to retrieve good reason to not use this method on images. So to compress the text the most encoding technique known is the Huffman Encoding which it will be explained in exhaustive way. In this manuscript will showed how to compute a text compression method on images in particular the method and the reason to choice a determinate image format against the other. The method studied and analyzed in this manuscript is the Re-Pair algorithm which is purely for grammatical context to be compress. At the and it will be showed the good result of this application.