A Note on Interference in Random Point Sets

Abstract: The (maximum receiver-centric) interference of a geometric graph (von Rickenbach etal (2005)) 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 Theta((\log n)^{1/2}).