We present polynomial-time algorithms for approximate counting and sampling solutions to
constraint satisfaction problems (CSPs) with atomic constraints within the local lemma …

We give new algorithms based on Markov chains to sample and approximately count
satisfying assignments to k-uniform CNF formulas where each variable appears at most d …

We give a Markov chain based algorithm for sampling almost uniform solutions of constraint
satisfaction problems (CSPs). Assuming a canonical setting for the Lovász local lemma …

We study the problem of sampling almost uniform proper $ q $-colourings in $ k $-uniform
simple hypergraphs with maximum degree $\Delta $. For any $\delta> 0$, if $ k\geq\frac {20 …

We introduce efficient algorithms for approximate sampling from symmetric Gibbs
distributions on the sparse random (hyper) graph. The examples we consider include (but …

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-
colorings for k-uniform hypergraphs with maximum degree Δ if k≥ 28 and q> 315Δ14/k− 14 …

The past decade has witnessed advancements in designing efficient algorithms for
approximating the number of solutions to constraint satisfaction problems (CSPs), especially …

All questions considered in this thesis are related to either some class of Random Graphs or
to a randomized algorithm or to both. The main property that is studied in Chapters 2, 3 & 4 …