Bounding flow-performance in probabilistic weighted networks

Much research has been done on computing connectivity-probability in probabilistic networks. More recently, the area has been expanded to other performance measures, such as maxflow and distance. These problems are, in general, NP-hard. Therefore efficiently computable, and accurate, lower and upper bounds are sought. This paper presents: 1) distance renormalization which generalizes the reliability renormalization algorithm of Harms and Colbourn for bounding probabilistic distances in bi-directional probabilistic weighted networks; and 2) a mechanism based on nonplanar duality for using this algorithm to bound probabilistic maxflow and mean maxflow. The results obtained via distance renormalization compare favorably with other current techniques for the authors' suite of test cases.