Abstract
We propose a new low-interference topology for wireless ad hoc networks modeled by Quasi Unit Disk Graphs. Our topology combines two existing structures, the relaxed Greedy structure developed by Damian, Pandit and Pemmaraju, and the low-interference structure developed by Burkhart, von Rickenbach, Wattenhofer and Zollinger. Our main contribution is showing that, when applied on a QUDG G = (V, E), this new structure inherits most properties of the two underlying structures: (i) it is a t(1 + e) spanner of G, for any t > 1 and e > 0, (ii) it has optimal interference among all t-spanners for G, (iii) it has O(1) maximum degree, (iv) its total weight is within a factor of O(log Δ) of the weight of a minimum spanning tree for V, where Δ is the aspect ratio of G, and (v) it can be implemented efficiently in O(log Δ + log*n) rounds of communication.
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