We review results on the scaling of the optimal path length l(opt) in random networks with weighted links or nodes. We refer to such networks as "weighted" or "disordered" networks. The optimal path is the path with minimum sum of the weights. In strong disorder, where the maximal weight along...

We consider the effect of network topology on the optimality of packet routing which is quantified by γc, the rate of packet insertion beyond which congestion and queue growth occurs. We show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators,...

In this paper, we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oilfield to breakthrough into a production well. The main contribution is to show that when these previously published results are used on realistic data they are in...

In this paper, we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oil field to breakthrough into a production well. The main contribution is to show that when these previously published results are used on realistic data they are in...

We numerically simulate the traveling time of a tracer in convective flow between two points (injection and extraction) separated by a distance r in a model of porous media, d=2 percolation. We calculate and analyze the traveling time probability density function for two values of the fraction...

We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length l of the optimal path scales with geometric distance r , as l approximately r (d(opt) with d(opt) =1.22+/-0.01 for d=2 and 1.44+/-0.02 for...

We study the current flow paths between two edges in a random resistor network on a Ltimes L square lattice. Each resistor has resistance e ax, where x is a uniformly-distributed random variable and a controls the broadness of the distribution. We find (a) the scaled variable uequiv L/a nu,...

To study transport properties of complex networks, we analyze the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)sim k -lambda in which each link has the same unit resistance. We predict a broad range of values of G, with...

We study the behavior of the optimal path between two sites separated by a distance r on a d-dimensional lattice of linear size L with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We...

We study the statistics of the optimal path in both random and scale-free networks, where weights are taken from a general distribution P(w). We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter (S defined as AL(-1/v) for...