Fast Insertion and Deletion in Compressed Texts

Abstract

Text compression techniques like bzip2 lack the possibility to delete the n th word or to insert text before the n th word of compressed texts without prior decompression of the compressed texts. We present a text compression technique that supports fast insertion into and deletion from compressed texts without full decompression of the compressed text. Our approach combines Indexed Reversible Transformation (IRT) [1], Run-Length-Encoding (RLE), and the Wavelet Tree (WT). For a reasonable size of inserted or deleted texts (more details are given in [2]), our approach is faster than modifying uncompressed text preceded by a decompression step and followed by a compression step.Let IRT(S) denote the Burrows-Wheeler-Transformation (BWT) applied to a text S according to an ordering relation A $ that fulfills the following conditions. The lexicographical order of the word delimiters '$' is changed in such a way, that all '$' of S get the smallest lexicographical order in A $ , and most important, the order of the word delimiters among themselves is determined by their occurrence in S from left to right. That is, the n th word delimiter '$' appearing in S gets a smaller lexicographical order in A $ than the n+1 st word delimiter '$'. Furthermore, IRT sorts characters of S according to their prefix (opposed to BWT that sorts them according to their suffix). Thus, in contrast to BWT, the first character of the n th word of S occurs at position n of IRT(S). This provides a selfindex to the first character of each word of S, which allows for the reconstruction of each word individually without retransforming IRT(S) in total [1].On IRT(S), we apply RLE that returns a bit-stream B and a string R. B is the run-length bit-vector of IRT(S) that contains a 0-bit for each character in IRT(S) that is equal to the previous character and a 1-bit otherwise. R is IRT(S) after reducing each run of equal characters within IRT(S) to one character. The WT W of R stores the bits of the Huffman codes of all characters c i of R, such that for each c i , (1) the Huffman code of c i is stored on a path from the root node to the leaf node representing c i in W, (2) one bit of the Huffman code of c i is stored on each node of the path to c i except for the leaf node, (3) if a 0-bit (1-bit) is stored in a node of W, the path continues with the left (right) sub-tree of W.To delete the n th word of S, we search, mark, and remove the bits of its letters from B and W. The search starts at position B[n] and uses Rank and Select functions [2] on B and the nodes of W to proceed to the bits representing the remaining characters of a word. The found bits are marked, and all unmarked bits represent the compressed text after deleting the n th word of S. To insert a word before the n th word of S into the compressed representation (B,W) of S, we could, reverse to deletion, letter by letter, search and mark the insert positions in B and W and insert the appropriate bits, which computes the compressed representation (B2,W2) of the result string S2. However, in...