A note on interference in random networks

The (maximum receiver-centric) interference of a geometric graph (von Rickenbach et al. 2005 [11]) is studied. It is shown that, with high probability, the following results hold for a set, V, of n points independently and uniformly distributed in the unit d-cube, for constant dimension d: (1) there exists a connected graph with vertex set V that has interference O((log⁡n)1/3); (2) no connected graph with vertex set V has interference o((log⁡n)1/4); and (3) the minimum spanning tree of V has interference Θ((log⁡n)1/2).