Synthesis of reliable networks in the presence of line failures

This paper is devoted to synthesis of reliable networks when nodes are perfect and links fail independently with the same probability. The All Terminal Reliability (ATR) model is used. When links are highly reliable the solution to the problem is known: it is a class of the so-called super-λ graphs. In this paper we concentrate on networks that are optimal independently on the links´ quality: super-λ graphs are searched for a graph that maximizes network reliability when links are very unreliable. We consider the class of regular graphs and show when it can be further limited to circulant ones. Contrary to the approach of other authors, we do not solve the problem analytically but use discrete approximate optimization techniques and obtain a solution, that most probably is very close to the optimal one