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The LZW compression standard is a simple to implement, and fairly good compression algorithm. It does not perform any statistical analysis of the input data and thus is not optimal, however it can see gains of around 20-30% on most natural language text of sufficient size. Other properties of the algorithm are its relatively efficient, stream-compatible encryption.
LZW compression should be used where you want to reduce the size of data by a modest amount with good performance and low memory overhead.
For more information regarding the algorithm you may view the Wikipedia page.