We prove a number of improved inaproximability results,
including the best up to date explicit approximation
thresholds for MIS problem of bounded degree, bounded
occurrences MAX-2SAT, and bounded degree Node Cover. We
prove also for the first time inapproximability of the
problem of Sorting by Reversals and display an explicit
approximation threshold. This last problem was proved only
recently to be NP-hard, in contrast to its signed version
which is computable in polynomial time.