In a series of recent works, Boyd, Diaconis, and their co-authors have
introduced a semidefinite programming approach for computing the fastest mixing
Markov chain on a graph of allowed transitions, given a target stationary
distribution. In this paper, we show that standard mixing-time analysis
techniques--variational characterizations, conductance, canonical paths--can be
used to give simple, nontrivial lower and upper bounds on the fastest mixing
time.