ALGOSENSORS 2010: Algorithms for Sensor Systems pp 1-15 | Cite as
Improved Local Algorithms for Spanner Construction
Conference paper
Abstract
Let S be a set of n points in the plane, let \({\cal E}\) be the complete Euclidean graph whose point-set is S, and let G be the Delaunay triangulation of S. We present a very simple local algorithm that, given G, constructs a subgraph of G of degree at most 11 that is a geometric spanner of G with stretch factor 2.86, and hence a geometric spanner of \({\cal E}\) with stretch factor < 7. This algorithm gives an \(O(n\lg{n})\) time centralized algorithm for constructing a subgraph of G that is a geometric spanner of \({\cal E}\) of degree at most 11 and stretch factor < 7.
The algorithm can be generalized to unit disk graphs to give a local algorithm for constructing a plane spanner of a unit disk graph of degree at most 11 and stretch factor < 7.
Keywords
spanners Delaunay triangulations unit disk graphsPreview
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