Localized Spanners for Ad Hoc Wireless Networks

We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G = (V ,E) and any ε > 0, a (1+ ε)-spanner for G of maximum degree O(1) and total weight O(ω(MST )), where ω(MST ) denotes the weight of a minimum spanning tree forV . 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 forG of maximum degree O(1) and total weight O(ω(MST )). Here Cdel denotes the stretch factor of the unit Delaunay triangulation for V . Both constructions can be completed in O(1) rounds of communication, and require each node to know its own coordinates.