We consider the problem of computing minimum congestion, fault‐tolerant, redundant assignments of messages to faulty, parallel delivery channels. In particular, we are given a set Kof faulty channels, each having an integer capacity ciand failing independently with probability fi . We are also given a set Mof messages to be delivered over K , and a fault‐tolerance constraint (1‐ϵ) , and we seek a redundant assignment ϕthat minimizes congestion \lilsf Cong(ϕ) , i.e. the maximum channel load, subject to the constraint that, with probability no less than (1‐ϵ) , all the messages have a copy on at least one active channel. We present a polynomial‐time 4‐approximation algorithm for identical capacity channels and arbitrary message sizes, and a 2 \lceil\ln(|K|/\e)/\ln(1/fmax ) ceil ‐approximation algorithm for related capacity channels and unit size messages.Both algorithms are based on computing a collection {K 1 , \ldots, K ν }of disjoint channel subsets such that, with probability no less than (1‐ϵ) , at least one channel is active in each subset. The objective is to maximize the sum of the minimum subset capacities. Since the exact version of this problem is NP ‐complete, we provide a 2‐approximation algorithm for identical capacities, and a polynomial‐time (8+ m o (1)) ‐approximation algorithm for arbitrary capacities.
