Wireless sensor networks can often be viewed in terms of a uniform deployment of a large
number of nodes in a region of Euclidean space. Following deployment, the nodes self-
organize into a mesh topology with a key aspect being self-localization. Having obtained a
mesh topology in a dense, homogeneous deployment, a frequently used approximation is to
take the hop distance between nodes to be proportional to the Euclidean distance between
them. In this work, we analyze this approximation through two complementary analyses. We …