Design of Minimal Fault Tolerant Networks: Asymptotic Bounds

This paper deals with the design of on board networks in satellites (also called Traveling wave tube Amplifiers (TWTA)). These networks should connect signals arriving on some ports of the satellite to amplifiers, even in case of failures of some amplifiers. They are made of links and expensive switches each with 4 links. So, the aim is to design networks having as few switches as possible and satisfying the following property: there exist p edge-disjoint paths from the p signals arriving on p+λ ports (inputs) to any set of p amplifiers (outputs) chosen from the p+k total number of outputs. We call such networks valid (p,λ,k)-networks and want to determine the minimum number of switches N (p,λ,k) of such networks. By symmetry we suppose λ ≤ k and we note n := p+k. We give tight results for small values of k and asymptotic results when k = O(logn) which are tight when k = Θ(λ) and when λ = 0.