What is a Viterbi algorithm that exploits sparseness of transition matrix?

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What is a Viterbi algorithm that exploits sparseness of transition matrix?

In

PYIN: A FUNDAMENTAL FREQUENCY ESTIMATOR USING PROBABILISTIC THRESHOLD DISTRIBUTIONS Matthias Mauch and Simon Dixon https://www.eecs.qmul.ac.uk/~simond/pub/2014/MauchDixon-PYIN-ICASSP2014.pdf

the authors write:

the HMM is decoded using an efficient version of the Viterbi algorithm that exploits the sparseness of the transition matrix.

I have not been able to find how such version differs from a typical Viterbi algorithm. I also speculated that it does not differ in implementation, but merely performs better by excluding all zero elements.