Lzip
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First released in version 1.0 in April of 2000, Lzip was touted by its authors as an advanced file compression utility that "generates smaller file sizes than either gzip or bzip2, and does so much faster". Lzip is based on a so-called "lossy" data compression scheme originally developed by Werner von Lessiss and R.T. Moore.[1]
[edit] Lzip compression
Lzip compression is based the "Lessiss-Moore algorithm" (LMA)[2] , described as "a two-pass bit-sieve to first remove all unimportant data from the data set". According to Lessiss and Moore, this was "implemented quite effectively by eliminating all of the 0's." The LMA then sorts the remaining bits into increasing order, and begins searching for patterns. The number of passes in this search is set to (10-N) in lzip, where N is the numeric command-line argument.
For every pattern of length (10/N) found in the data set, the algorithm makes a mark in its hash table. By keeping the hash table small, memory overhead is kept low. Lzip uses a two-entry hash table. Then data in this table is then plotted in three dimensions, and a discrete cosine transform transforms it into frequency and amplitude data. This data is filtered for sounds that are beyond the range of the human ear, and the result is transformed back (via an indiscrete cosine) into the hash table, in random order. The final step in the LMA algorithm involves taking each pattern in the original data set, XOR'ing it with the log of its entry in the new hash table, shuffling each byte two positions to the left.
[edit] Lzip "de-compression"
Lzip developers used what they called the "Warren Interior Point Method" to step backwards through the cosine transform. Alternatively referred to as the Warren "Dice-Prayer" method, it was described as a solution to "OR problems when you don't have the time or perhaps the willpower to work through Simplex".
R.T. Moore admitted that his application of this "Dice-prayer" method to the problem was not straightforward, and that the mathematical proof of the algorithm remained incomplete. Moore nonetheless asserted that that the addition of fast Monte Carlo sorting -- combined with long-established proof from physics that Albert Einstein's claim, "God does not play dice with the universe" had been totally refuted, was sufficient evidence for the validity of the "Dice-Prayer" hypothesis. In this context, Lessis and Moore named the decompression method "the PLACeBO algorithm".
