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arXiv · 1705.01465

The Homogeneous Broadcast Problem in Narrow and Wide Strips

Mark de Berg·Hans L. Bodlaender·Sándor Kisfaludi-Bak
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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 $s\in P$ 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 $w$.

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Mark de Berg, Hans L. Bodlaender, Sándor Kisfaludi-Bak. 2017-05-03. The Homogeneous Broadcast Problem in Narrow and Wide Strips. https://arxiv.org/abs/1705.01465

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