Localized Spanners for Ad Hoc Wireless Networks

We present a new efficient localized algorithm to construct, for any given quasi-unit disk graphG = (V , E) and anyε > 0, a(1+ ε)-spanner forG of maximum degreeO(1) and total weightO(ω(MST )), whereω(MST ) denotes the weight of a minimum spanning tree for V . We further show that similar localized techniques can be used to construct, for a given unit disk graphG = (V , E), a planarCdel(1+ε)(1+ π2 )-spanner for G of maximum degreeO(1) and total weightO(ω(MST )). HereCdel denotes the stretch factor of the unit Delaunay triangulation for V . Both constructions can be completed inO(1) rounds of communication, and require each node to know its own coordinates.

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