This paper presents new results on parallel constructions of the
length-limited prefix-free codes with the minimum redundancy.
We describe an algorithm for the construction of length-limited codes
that works in $O(L)$ time with $n$ processors for $L$ the
maximal codeword length.
We also describe an algorithm for a construction ... more >>>

We consider sets of strings with high Kolmogorov complexity, mainly
in resource-bounded settings but also in the traditional
recursion-theoretic sense. We present efficient reductions, showing
that these sets are hard and complete for various complexity classes.

In particular, in addition to the usual Kolmogorov complexity measure
K, ... more >>>

Given a $k$-uniform hypergraph, the E$k$-Vertex-Cover problem is
to find a minimum subset of vertices that ``hits'' every edge. We
show that for every integer $k \geq 5$, E$k$-Vertex-Cover is
NP-hard to approximate within a factor of $(k-3-\epsilon)$, for
an arbitrarily small constant $\epsilon > 0$.

This almost matches the ... more >>>