We investigate the computational hardness of the {\sc Connectivity},
the {\sc Strong Connectivity} and the {\sc Broadcast} type of Range
Assignment Problems in $\R^2$ and $\R^3$.
We present new reductions for the {\sc Connectivity} problem, which
are easily adapted to suit the other two problems. All reductions
are considerably simpler ... more >>>

Let $d \geq d_0$ be a sufficiently large constant. A $(n,d,c
\sqrt{d})$ graph $G$ is a $d$ regular graph over $n$ vertices whose
second largest eigenvalue (in absolute value) is at most $c
\sqrt{d}$. For any $0 < p < 1, ~G_p$ is the graph induced by
retaining each edge ... more >>>

We show that for any reasonable semantic model of computation and for
any positive integer $a$ and rationals $1 \leq c < d$, there exists a language
computable in time $n^d$ with $a$ bits of advice but not in time $n^c$
with $a$ bits of advice. A semantic ... more >>>