The PPSZ algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable $3$-SAT formulas can be found in expected running time at most $\Oc(1.3071^n).$ Using the technique of limited independence, we can derandomize this algorithm yielding $\Oc(1.3071^n)$ ... more >>>

Can NP-complete problems be solved efficiently in the physical universe?
I survey proposals including soap bubbles, protein folding, quantum
computing, quantum advice, quantum adiabatic algorithms,
quantum-mechanical nonlinearities, hidden variables, relativistic time
dilation, analog computing, Malament-Hogarth spacetimes, quantum
gravity, closed timelike curves, and "anthropic computing." The ... more >>>

Mergers are functions that transform k (possibly dependent)
random sources into a single random source, in a way that ensures
that if one of the input sources has min-entropy rate $\delta$
then the output has min-entropy rate close to $\delta$. Mergers
have proven to be a very useful tool in ... more >>>