Brief Announcement: Hierarchical Neighbor Graphs: A Sparse Connected Structure for Euclidean Point Sets
In this paper we introduce a new randomized method for constructing a bounded degree connected structure on points in Euclidean space: p-hierarchical neighbor graphs. The structure has a flavor of hierarchical clustering and requires only local knowledge and minimal computation at each node to be formed and repaired. Hence it is a suitable interconnection model for an ad hoc wireless network. Our structure has expected constant degree, diameter logarithmic in the size of the set and good spanner-like properties in a probabilistic sense.
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