Variable length path coupling

We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path coupling theorem of Bubley and Dyer, allowing the defining partial couplings to have length determined by a random stopping time. Unlike the original path coupling theorem, our version can produce multi-step (non-Markovian) couplings. Using our variable length path coupling theorem, we improve the upper bound on the mixing time of the Glauber dynamics for randomly sampling colorings.

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Thomas P. Hayes, Eric Vigoda
• Keywords: Algorithms, Finite Markov Chains, Original Path Coupling, Path Coupling Theorem, SODA 2004