Interval routing in reliability networks

The results are extended to random meshes of higher dimension. We show that, asymptotically almost surely, the number of intervals per edge for a random r-dimensional mesh with n nodes is Ω(16-r(δ+2)1-rr-4(logn)1-1/r), for every additive stretch δ⩾0 and for every integral dimension r∈[1,log2n].