Let \calK be a simplicial complex and g the rank of its p-th homology group \sfH_p(\calK)
defined with ℤ 2 coefficients. We show that we can compute a basis H of \sfH_p(\calK) and …

We study a combinatorial geometric problem related to the design of wireless networks with
directional antennas. Specifically, we are interested in necessary and sufficient conditions …

We introduce a new structure for a set of points in the plane and an angle α α, which is
similar in flavor to a bounded-degree MST. We name this structure α α-MST. Let P be a set of …

Underwater environments have never been much of a constraint to the rich animal life they
support at all depths of our seas and oceans. Indeed, nature has taken advantage of this …

Graph augmentation problems are motivated by network design and have been studied
extensively in optimization. We consider augmentation problems over plane geometric …

Digital media manipulation has become easily performed at personal level with the rapidly
growth of Technology. Presenting an issue of protecting digital media integrity …

Let P be a set of points in the plane, representing transceivers equipped with a directional
antenna of angle α and range r. The coverage area of the antenna at point p is a circular …

Connectivity in wireless sensor networks may be established using either omnidirectional or
directional antennae. The former radiate power uniformly in all directions while the latter …

For any angle α< 2 π, we show that any connected communication graph that is induced by
a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a …

Given a set S of n sensors in the plane we consider the problem of establishing an ad hoc
network from these sensors using directional antennae. We prove that for each given integer …