Minimizing Congestion of Layouts for ATMNetworks

We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete network K n of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any connguration of up to f layouts and have the least possible congestion. First, we study the minimal congestion of 1-hop f-tolerant layouts in K n. For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network K n F] which results from K n by deleting links from a set F of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in K n , for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution. Links fail independently with constant probability p < 1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p < 1, we show such layouts in K n , with congestion O(log n).