The homogeneous broadcast problem in narrow and wide strips

Abstract

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.