Let P be a set of nodes in a wireless network, where each node is modeled
as a point in the plane, and let s∈P be a given source node. Each node p
can transmit information to all other nodes within unit distance, provided p
is activated. The (homogeneous) broadcast problem is to activate a minimum
number of nodes such that in the resulting directed communication graph, the
source s can reach any other node. We study the complexity of the regular and
the hop-bounded version of the problem (in the latter, s must be able to
reach every node within a specified number of hops), with the restriction that
all points lie inside a strip of width w. We almost completely characterize
the complexity of both the regular and the hop-bounded versions as a function
of the strip width w.Comment: 50 pages, WADS 2017 submissio