Improved inaproximability results are given, including the
best up to date explicit approximation thresholds for bounded
occurence satisfiability problems, like MAX-2SAT and E2-LIN-2,
and problems in bounded degree graphs, like MIS, Node Cover
and MAX CUT. We prove also for the first time inapproximability
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We study small degree graph problems such as Maximum Independent Set
and Minimum Node Cover and improve approximation lower bounds for
them and for a number of related problems, like Max-B-Set Packing,
Min-B-Set Cover, Max-Matching in B-uniform 2-regular hypergraphs.
For example, we prove NP-hardness factor of 95/94
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A $k$-uniform hypergraph $G$ of size $n$ is said to be $\varepsilon$-far from having an independent set of size $\rho n$ if one must remove at least $\varepsilon n^k$ edges of $G$ in order for the remaining hypergraph to have an independent set of size $\rho n$. In this work, ... more >>>

We give a new method for analysing the mixing time of a Markov chain using
path coupling with stopping times. We apply this approach to two hypergraph
problems. We show that the Glauber dynamics for independent sets in a
hypergraph mixes rapidly as long as the maximum degree $\Delta$ of ... more >>>

We prove almost tight hardness results for finding independent sets in bounded degree graphs and hypergraphs that admit a good
coloring. Our specific results include the following (where $\Delta$, assumed to be a constant, is a bound on the degree, and
$n$ is the number of vertices):

\begin{itemize}
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