Randomized algorithms have become a central part of the algorithms curriculum based on
their increasingly widespread use in modern applications. This book presents a coherent …

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis
Gharan) from the Boolean domain to general discrete domains. This property characterises …

We study the mixing time of the Glauber dynamics for general spin systems on the regular
tree, including the Ising model, the hard‐core model (independent sets), and the …

A well-known conjecture in computer science and statistical physics is that Glauber
dynamics on the set of k-colorings of a graph G on n vertices with maximum degree Δ is …

We analyze Markov chains for generating a random k‐coloring of a random graph Gn, d/n.
When the average degree d is constant, a random graph has maximum degree Θ (log n/log …

There exist several applications of sensor networks where the reliability of data delivery can
be critical. Although the redundancy inherent in a sensor network might increase the degree …

We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling
(proper) k-colorings of an input graph G on n vertices with maximum degree/spl Delta/and …

In recent years there has been considerable progress on the analysis of Markov chains for
generating a random coloring of an input graph. These improvements have come in …

We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting
the number of q-colorings of a graph of maximum degree Delta, provided only that q≥ …

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for
computing the partition function of a two-state spin system on an arbitrary graph, when the …