Consider $n$ sensors whose positions are represented by $n$ uniform,
independent and identically distributed random variables assuming values in the
open unit interval $(0,1)$. A natural way to guarantee connectivity in the
resulting sensor network is to assign to each sensor as its range, the maximum
of the two possible distances to its two neighbors. The interference at a given
sensor is defined as the number of sensors that have this sensor within their
range. In this paper we prove that the expected maximum interference of the
sensors is $\Theta (\sqrt{\ln n})$.

In this paper we consider query versions of visibility testing and visibility
counting. Let $S$ be a set of $n$ disjoint line segments in $\R^2$ and let $s$
be an element of $S$. Visibility testing is to preprocess $S$ so that we can
quickly determine if $s$ is visible from a query point $q$. Visibility counting
involves preprocessing $S$ so that one can quickly estimate the number of
segments in $S$ visible from a query point $q$.

A memoryless routing algorithm is one in which the decision about the next
edge on the route to a vertex t for a packet currently located at vertex v is
made based only on the coordinates of v, t, and the neighbourhood, N(v), of v.
The current paper explores the limitations of such algorithms by showing that,
for any (randomized) memoryless routing algorithm A, there exists a convex
subdivision on which A takes Omega(n^2) expected time to route a message
between some pair of vertices.