Преобразование "Перемещение в начало" (MTF): Принципы и применение.

The move to front (MTF) transform is an encoding of data (typically a stream of bytes) designed to improve the performance of entropy encoding techniques of compression. When efficiently implemented, it is fast enough that its benefits usually justify including it as an extra step in data compression algorithm. This algorithm was first published by Boris Ryabko under the name of "book stack" in 1980. Subsequently, it was rediscovered by J. K. Bentley et al. in 1986, as attested in the explanatory note.

Details of implementation are important for performance, particularly for decoding. For encoding, no clear advantage is gained by using a linked list, so using an array to store the list is acceptable, with worst case performance O(nk), where n is the length of the data to be encoded and k is the number of values (generally a constant for a given implementation). The typical performance is better because frequently used symbols are more likely to be at the front and will produce earlier hits. This is also the idea behind a Move to front self organizing list. However, for decoding, we can use specialized data structures to greatly improve performance.

The MTF transform takes advantage of local correlation of frequencies to reduce the entropy of a message. Indeed, recently used letters stay towards the front of the list; if use of letters exhibits local correlations, this will result in a large number of small numbers such as "0"'s and "1"'s in the output. However, not all data exhibits this type of local correlation, and for some messages, the MTF transform may actually increase the entropy. An important use of the MTF transform is in Burrows–Wheeler transform based compression. The Burrows–Wheeler transform is very good at producing a sequence that exhibits local frequency correlation from text and certain other special classes of data. Compression benefits greatly from following up the Burrows–Wheeler transform with an MTF transform before the final entropy encoding step.

As an example, imagine we wish to compress Hamlet's soliloquy (To be, or not to be ). We can calculate the size of this message to be 7033 bits. Naively, we might try to apply the MTF transform directly. The result is a message with 7807 bits (higher than the original). The reason is that English text does not in general exhibit a high level of local frequency correlation. However, if we first apply the Burrows–Wheeler transform, and then the MTF transform, we get a message with 6187 bits. Note that the Burrows–Wheeler transform does not decrease the entropy of the message; it only reorders the bytes in a way that makes the MTF transform more effective. One problem with the basic MTF transform is that it makes the same changes for any character, regardless of frequency, which can result in diminished compression as characters that occur rarely may push frequent characters to higher values. Various alterations and alternatives have been developed for this reason. One common change is to make it so that characters above a certain point can only be moved to a certain threshold. Another is to make some algorithm that runs a count of each character's local frequency and uses these values to choose the characters' order at any point. Many of these transforms still reserve zero for repeat characters, since these are often the most common in data after the Burrows Wheeler Transform.

The term Move To Front (MTF) is also used in a slightly different context, as a type of a dynamic linked list. In an MTF list, each element is moved to the front when it is accessed. This ensures that, over time, the more frequently accessed elements are easier to access.