In this paper, we propose a proactive recovery method against multiple network failures for large-scale packet switching networks. The proposed method exploits the overlay networking technique. Specifically, it constructs multiple logical network topologies from the original overlay network topology by assuming various failure patterns. When a failure is detected, our method selects one topolog...

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation resul...

We present a novel framework for evaluating recommendation algorithms in terms of the ‘jumps’ that they make to connect people to artifacts. This approach emphasizes reachability via an algorithm within the implicit graph structure underlying a recommender dataset, and serves as a complement to evaluation in terms of predictive accuracy. The framework allows us to consider questions relating al...

We consider the path length in decision diagrams for multiple-valued functions. This is an important measure of a decision diagram, since this models the time needed to evaluate the function. We focus on the average path length (APL), which is the sum of the path lengths over all assignments of values to the variables divided by the number of assignments. First, we show a multiple-valued functi...

Is it possible to treat large scale distributed systems as physical systems? The importance of that question stems from the fact that the behavior of many P2P systems is very complex to analyze analytically, and simulation of scales of interest can be prohibitive. In Physics, however, one is accustomed to reasoning about large systems. The limit of very large systems may actually simplify the a...

where sA„ is the average length of path for the electrons traversing the foil. The approximation involved in (1) is therefore equivalent to the assumption of linearity of the electron paths and the Goudsmit-Saunderson result is thus valid only for thin foils or for very fast electrons for which the scattering of the beam is small. Stated otherwise, the assumption of linear paths is equivalent t...

We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone errorcorrecting codes, and show that hardness amplification for NP is essentially equivalent to constructing efficiently locally encodable and locally list-decodable monotone codes. The previous hardness amplification resul...

We introduce a minimal model of growing small-world network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient C = 3 2 ln3− 1 ≈ 0.6479, which are in good agreement with the numerical simulations. We also prove that the i...

The average shortest path distance ` between all pairs of nodes in real-world networks tends to be small compared to the number of nodes. Providing a closed-form formula for ` remains challenging in several network models, as shown by recent papers dedicated to this sole topic. For example, Zhang et al. proposed the deterministic model ZRG and studied an upper bound on `. In this paper, we use ...

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter (r) sets the length scale over which shortcuts are uniformly distributed. When r = 0 we have an ordered network, whereas r = 1 corresponds to the original SWN model. These short-range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenom...