We propose to introduce redundant interconnects for manufacturing yield and reliability improvement. By introducing redundant interconnects, the potential for open faults is reduced at the cost of increased potential for short faults; overall, manufacturing yield and fault tolerance can be improved. We focus on a post-processing, tree augmentation approach which can be easily integrated in current physical design flows. Our contributions are as follows: We formulate the problem as a variant of the classical 2-edge-connectivity augmentation problem in which we take into account such practical issues as wirelength increase budget, routing obstacles, and use of Steiner points. We show that an optimum solution can always be found on the Hanan grid defined by the terminals and the corners of the feasible routing region. We give a compact integer program formulation which is solved in practical runtime by the commercial optimization package CPLEX for nets with up to 100 terminals. We give a well-scaling greedy algorithm which has practical runtime up to 1,000 terminals, and comes on the average within 1-2 % of the optimum computed by CPLEX. We give a comprehensive experimental study comparing the solution quality and runtime of our methods with the best methods reported in the literature for the related 2-edge-connectivity augmentation problem, including a sophisticated heuristic based on minimum-weight branchings [11] and a recent genetic algorithm [17]. Experiments on randomly generated and industry testcases show that our greedy augmentation method achieves significant increase in reliability (as measured by the percentage of biconnected tree edges) with very small increase in wirelength. For example, on 1,000 terminal nets the average percentage of biconnected tree edges is 34 ¡ 19 % for a wirelength increase of only 1%, and 87 ¡ 73 % for a wirelength increase of 20%. SPICE simulations on industry routed nets show that non-tree routing has the additional benefit of reducing maximum sink delay by an average of 28 ¡ 26 % compared to Steiner routing, and by an average of 3 ¡ 72 % compared to timing optimized routing. SPICE simulations further imply that non-tree routing has smaller delay variation due to process variability. I.

This paper considers the problem of augmenting a given graph by a cheapest possible set of addi-tional edges in order to make the graph vertex-biconnected. A real-world instance of this problem is the enhancement of an already established computer network to become robust against single node failures. The presented memetic algorithm includes effective preprocessing of problem data and a fast local improvement strategy which is applied before a solution is included into the population. In this way, the memetic algorithm’s population consists always of only feasible, locally optimal solution candidates. Empirical results on two sets of test instances indicate the superiority of the new approach over two previous heuristics and an earlier genetic algorithm.

Abstract. We consider a possible scenario of experimental analysis on heuristics for optimization: identifying the contribution of local search components when algorithms are evaluated on the basis of solution quality attained. We discuss the experimental designs with special focus on the role of the test instances in the statistical analysis. Contrary to previous practice of modeling instances as a blocking factor, we treat them as a random factor. Together with algorithms, or their components, which are fixed factors, this leads naturally to a mixed ANOVA model. We motivate our choice and illustrate the application of the mixed model on a study of local search for the 2-edge-connectivity problem. 1

This paper considers the problem of augmenting a given graph by a cheapest possible set of additional edges in order to make the graph vertex-biconnected. A real-world instance of this problem is the enhancement of an already established computer network to become robust against single node failures. The presented memetic algorithm includes an effective preprocessing of problem data and a fast local improvement strategy which is applied during initialization, mutation, and recombination. Only feasible, locally optimal solutions are created as candidates.

We consider the 2-edge-connectivity augmentation problem: given a graph S = (V, E) which is not 2-edge-connected and a set of new edges E ′ ⊆ V × V with non-negative weights, find a minimum cost subset X of E ′ such that adding the edges of X to S results in a 2-edge-connected graph. A practical application is the extension of an existing telecommunication network to become robust against single link failures. We compare, experimentally, different algorithms for solving general and large-scale instances. This includes exact methods based on mathematical programming, simple construction heuristics and metaheuristics. As part of the design of heuristics, we consider different neighborhood structures for local search, among which a very large scale neighborhood. In all cases, we exploit approaches through the graph formulation as well as through an equivalent set covering formulation. The results indicate that exact solutions by means of a basic integer programming model can be obtained in reasonably short time even on networks with 800 vertices and around 287.000 edges. Alternatively, an advanced heuristic algorithm based on subgradient optimization and iterated greedy finds often the optimal solution and is very fast. All previous benchmark instances are easily solved to optimality and new, larger, instances are introduced and studied.

It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work insisted on the fact that power-law degree distributions induce high resilience to random failure but high sensitivity to attack strategies, while Poisson degree distributions are quite sensitive in both cases. Then, much work has been done to extend these results. We aim here at studying in depth these results, their origin, and limitations. We review in detail previous contributions and give full proofs in a unified framework, and identify the approximations on which these results rely. We then present new results aimed at enlightening some important aspects. We also provide extensive rigorous experiments which help evaluate the relevance of the analytic results. We reach the conclusion that, even if the basic results of the field are clearly true and important, they are in practice much less striking than generally thought. The differences between random failures and attacks are not so huge and can be explained with simple facts. Likewise, the differences in the behaviors induced by power-law and Poisson distributions are not as striking as often claimed.