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Lossless Data Compression Algorithms 441
LZ78 algorithm creates a dictionary of codes that consist of the same size,
the LZW algorithm creates a dictionary of codes of different sizes.
When compressing text, the LZW algorithm starts out by creating a dictionary
of individual letters. Assuming all uppercase letters, A would be represented
by 1, B by 2, and so on. However, substituting a number for a single
character isn’t likely to save much space, so the LZW algorithm continues
examining the text for repetitive multiple-character strings to store as a
number, such as AB, ABC, ABCD, and so on.
Like most compression algorithms, the LZW algorithm works best on data
that contains redundant information, like this:
IAMSAMSAMIAM#
First, the LZW algorithm creates a dictionary of single characters represented
by numbers. I gets stored as 9, A as 1, M as 13, and S as 19.
When the LZW algorithm finds the second letter A, it doesn’t encode the letter
A all over again because it’s done that once already. Instead, the algorithm
encodes the next two characters, which happen to be AM, and assigns this twocharacter
combination to the next available number, which is 27. (Numbers 1
through 26 are assigned to the individual letters of the alphabet.)
When the algorithm sees the letter S again, it encodes the next two-character
string, SA, as the number 28. Then it finds the letter M again, so it encodes
the next two-character string, MI, as the number 29. Finally, it sees the letter
A again, so it checks the next two-character string, which is AM. Because the
algorithms already encoded AM before (as the number 27), the algorithm
expands to encode the three-character string, AM#, as the number 30, as
shown in Figure 4-4.
At the beginning of data, the LZW algorithm isn’t very efficient because it’s
slowly creating its dictionary. When the algorithm’s dictionary grows with
larger amounts of redundant data, it can replace these large chunks of redundant
data with small number codes.
Book IV
Chapter 4
The LZW algorithm is used to compress graphic images stored in the Graphic
Interchange Format (GIF). Originally, this algorithm was patented in 1985 and
the patent holder, Unisys, demanded royalties from software companies that
sold programs that could create GIF files. This patent problem caused computer
scientists to create and promote an alternate graphics format —
Portable Network Graphics (PNG). However, the PNG format never replaced
the GIF file format, especially after the LZW patent expired on June 20, 2003.
Data Compression
Algorithms