Redundancy and Algorithms

Most compression programs use a variation of the LZ adaptive dictionary-based algorithm to shrink files. "LZ" refers to Lempel and Ziv, the algorithm's creators, and "dictionary" refers to the method of cataloging pieces of data.

The system for arranging dictionaries varies, but it could be as simple as a numbered list. When we go through Kennedy's famous words, we pick out the words that are repeated and put them into the numbered index. Then, we simply write the number instead of writing out the whole word.

So, if this is our dictionary:

  1. ask
  2. what
  3. your
  4. country
  5. can
  6. for
  7. you

Our sentence now reads:  "1 not 2 3 4 5 6 7 8 -- 1 2 8 5 6 7 3 4"

If you knew the system, you could easily reconstruct the original phrase using only this dictionary and number pattern. This is what the expansion program on your computer does when it expands a downloaded file. You might also have encountered compressed files that open themselves up. To create this sort of file, the programmer includes a simple expansion program with the compressed file. It automatically reconstructs the original file once it's downloaded.

But how much space have we actually saved with this system? "1 not 2 3 4 5 6 7 8 -- 1 2 8 5 6 7 3 4" is certainly shorter than "Ask not what your country can do for you; ask what you can do for your country;" but keep in mind that we need to save the dictionary itself along with the file.

In an actual compression scheme, figuring out the various file requirements would be fairly complicated; but for our purposes, let's go back to the idea that every character and every space takes up one unit of memory. We already saw that the full phrase takes up 79 units. Our compressed sentence (including spaces) takes up 37 units, and the dictionary (words and numbers) also takes up 37 units. This gives us a file size of 74, so we haven't reduced the file size by very much.

But this is only one sentence! You can imagine that if the compression program worked through the rest of Kennedy's speech, it would find these words and others repeated many more times. And, as we'll see in the next section, it would also be rewriting the dictionary to get the most efficient organization possible.