In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. We show that greedy graph drawing schemes exist for the Euclidean metric in R, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits. Moreover...

Abstract The handy biometric data is a double-edged sword, paving the way of prosperity authentication systems but bringing personal privacy concern. To alleviate concern, various template protection schemes are proposed to protect from information leakage. preponderance existing proposals based on Hamming metric, which ignores fact that predominantly deployed recognition (e.g. face, voice, gai...

The study of finite metrics is an important area of research, because of its wide applications to many different problems. The input of many problems (for instance clustering, near-neighbor queries and network routing) naturally involves a set of points on which a distance function has been defined. Hence, one would be motivated to store and process metrics in an efficient manner. The central i...

The theory of sparse graph limits concerns itself with versions of local convergence and global convergence, see e.g. [41]. Informally, in local convergence we look at a large neighborhood around a random uniformly chosen vertex in a graph and in global convergence we observe the whole graph from afar. In this note rather than surveying the general theory we will consider some concrete examples...

We analyze directed, unweighted graphs obtained from xi ∈ R by connecting vertex i to j iff |xi − xj | < ε(xi). Examples of such graphs include k-nearest neighbor graphs, where ε(xi) varies from point to point, and, arguably, many real-world graphs such as copurchasing graphs. We ask whether we can recover the underlying Euclidean metric ε(xi) and the associated density p(xi) given only the dir...

In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. In this paper, we study greedy geometric routing in R, using the standard Euclidean metric. Greedy geometric routing is not always possible in fixed-dimensional Euclidean spaces, of course, as is the ...