Brief announcement: hierarchical neighbor graphs: a sparse connected structure for Euclidean point sets

Authors:
Amitabha Bagchi;Adit Madan;Achal Premi
Affiliations:
Indian Institute of Technology, New Delhi, India;Indian Institute of Technology, New Delhi, India;Indian Institute of Technology, New Delhi, India
Venue:
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Year:
2010

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Abstract

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.