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Kautz sequence generator

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Kautz sequence generator

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26 Apr 2011 (Updated )

Generates example Kautz sequences of specified number of characters and subsequence lengths.

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Description

The Kautz sequence is of the same family of sequences as the de Bruijn sequence, but has an additional requirement that it not contain any consecutive repeats of the same character.

The sequence is, by nature, circular, so the final members of pairs (or triplets, quadruplets, etc...) are found wrapped around to the beginning of the sequence.
 
Example:

>> sequence = kautz_generator(3,3)'

 sequence =
     3 1 3 2 1 2 1 3 1 2 3 2

 A sequence of N characters with a subsequence length of L would be
 ---------------------------------------------
 N*(N-1)^(L-1)characters in length, and would contain:
 N^(L-1) examples of each character,
 N^(L-2) examples of each pair of characters,
 N^(L-3) examples of each possible triplet of characters,
 and so on.
 ---------------------------------------------

Computation times will be *considerable* and unpredictable for large numbers of characters (>10)and subsequence lengths (>4). Sometimes the code will be unable to compute a solution and will restart. This restart is initiated when the total computation time exceeds time taken before the first backtrack times a multiplier of 4 (arrived at empirically).

If you find this useful and use it for research, please cite:
Brimijoin WO, McShefferty D, Akeroyd MA. J Acoust Soc Am. 2010 Jun;127(6):3678-88.

Acknowledgements

Combn (4.3) inspired this file.

MATLAB release MATLAB 7.10 (R2010a)
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Updates
29 Apr 2011

Title change

22 Jul 2011

Added acknowledgment to COMBN (jos)

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