Keitha Murray

Communications network reliability analysis approximations and bounds

The authors present a number of techniques based on tie-sets and cut-sets for bounding and approximating the 2-terminal reliability of a communications network model, with the knowledge that the 2-terminal reliability problem is NP-complete. Three classes of approximations are treated theoretically and in terms of examples. One method uses all the network cut-sets, but truncates the reliability expansion, leading to upper and lower bounds. Another method chooses subsets of the tie-sets and cut-sets, including the shorter (fewer element) tie-sets and cut-sets, and carries out the entire expansion. The third approximation technique incorporates features of both of the first two methods. The reduced tie-set and cut-set method, although exponential in the number of tie-sets and cut-sets of the network in theory, is polynomial in practice and provides lower and upper bounds of the same order of magnitude in most instances. The combined method has been shown to be polynomial in the number of 1, 2, and 3-edge cut-sets used and to run faster than the reduced tie-set and cut-set method.<<ETX>>

Bicliques in Graphs with Correlated Edges: From Artificial to Biological Networks

Networks representing complex biological interactions are often very intricate and rely on algorithmic tools for thorough quantitative analysis. In bi-layered graphs, identifying subgraphs of potential biological meaning relies on identifying bicliques between two sets of associated nodes, or variables – for example, diseases and genetic variants. Researchers have developed multiple approaches for forming bicliques and it is important to understand the features of these models and their applicability to real-life problems. We introduce a novel algorithm specifically designed for finding maximal bicliques in large datasets. In this study, we applied this algorithm to a variety of networks, including artificially generated networks as well as biological networks based on phenotype-genotype and phenotype-pathway interactions. We analyzed performance with respect to network features including density, node degree distribution, and correlation between nodes, with density being the major contributor to computational complexity. We also examined sample bicliques and postulate that these bicliques could be useful in elucidating the genetic and biological underpinnings of shared disease etiologies and in guiding hypothesis generation. Moving forward, we propose additional features, such as weighted edges between nodes, that could enhance our study of biological networks.