Damaged BZip Files Are Difficult to Repair

摘要

Bzip is a program written by Julian Seward that is often used under Unix to compress single files. It splits the file into blocks which are compressed individually using a combination of the Burrows-Wheeler-Transformation, the Move-To-Front algorithm, Huffman and Runlength encoding. The author himself stated that compressed blocks that are damaged, i.e., part of which are lost, are essentially non-recoverable. This paper gives a formal proof that this is indeed true: focusing on the Burrows-Wheeler-Transformation, the problem of completing a transformed string, such that the decoded string obeys certain file format restrictions, is NP-hard.