Recently, Raz established exponential lower bounds on the size
of resolution proofs of the weak pigeonhole principle. We give another
proof of this result which leads to better numerical bounds. Specifically,
we show that every resolution proof of $PHP^m_n$ must have size
$\exp\of{\Omega(n/\log m)^{1/2}}$ which implies an
$\exp\of{\Omega(n^{1/3})}$ bound when ... more >>>

In sequencing by hybridization (SBH),
one has to reconstruct a sequence
from its $l$-long substrings.
SBH was proposed as
an alternative to
gel-based
DNA sequencing approaches, but in its original form the method
is
not competitive.
Positional SBH (PSBH) is a recently proposed
enhancement ... more >>>

This paper studies the existence of efficient (small size)
amplifiers for proving explicit inaproximability results for bounded degree
and bounded occurrence combinatorial optimization problems, and gives
an explicit construction for such amplifiers. We use this construction
also later to improve the currently best known approximation lower bounds
more >>>