Generalizing Kronecker graphs in order to model searchable networks

This paper describes an extension to stochastic Kronecker graphs that provides the special structure required for searchability, by defining a “distance”-dependent Kronecker operator. We show how this extension of Kronecker graphs can generate several existing social network models, such as the Watts-Strogatz small-world model and Kleinberg’s latticebased model. We focus on a specific example of an expanding hypercube, reminiscent of recently proposed social network models based on a hidden hyperbolic metric space, and prove that a greedy forwarding algorithm can find very short paths of length O((log log n)^2) for graphs with n nodes

Distance-Dependent Kronecker Graphs for Modeling Social Networks

This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kronecker-like operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any lattice-based network model with sufficiently small distance-dependent connection probability will have a Poisson degree distribution and provide a general framework to prove searchability for such a network. Using this framework, we focus on a specific example of an expanding hypercube and discuss the similarities and differences of such a model with recently proposed network models based on a hidden metric space. We also prove that a greedy forwarding algorithm can find very short paths of length O((log log n)^2) on the hypercube with n nodes, demonstrating that distance-dependent Kronecker graphs can generate searchable network models

Methods and problems of wavelength-routing in all-optical networks

We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions

Multilingual manager: a new strategic role in organizations

Today?s knowledge management (KM) systems seldom account for language management and, especially, multilingual information processing. Document management is one of the strongest components of KM systems. If these systems do not include a multilingual knowledge management policy, intranet searches, excessive document space occupancy and redundant information slow down what are the most effective processes in a single language environment. In this paper, we model information flow from the sources of knowledge to the persons/systems searching for specific information. Within this framework, we focus on the importance of multilingual information processing, which is a hugely complex component of modern organizations

Quantum fast-forwarding: Markov chains and graph property testing

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with P the Markov chain transition matrix and D=P∘PT its discriminant matrix (D=P if P is symmetric), we construct a quantum walk algorithm that for any quantum state |v⟩ and integer t returns a quantum state ϵ-close to the state Dt|v⟩/∥Dt|v⟩∥. The algorithm uses O(∥Dt|v⟩∥−1tlog(ϵ∥Dt|v⟩∥)−1√) expected quantum walk steps and O(∥Dt|v⟩∥−1) expected reflections around |v⟩. This shows that quantum walks can accelerate the transient dynamics of Markov chains, complementing the line of results that proves the acceleration of their limit behavior. We show that this tool leads to speedups on random walk algorithms in a very natural way. Specifically we consider random walk algorithms for testing the graph expansion and clusterability, and show that we can quadratically improve the dependency of the classical property testers on the random walk runtime. Moreover, our quantum algorithm exponentially improves the space complexity of the classical tester to logarithmic. As a subroutine of independent interest, we use QFF for determining whether a given pair of nodes lies in the same cluster or in separate clusters. This solves a robust version of s-t connectivity, relevant in a learning context for classifying objects among a set of examples. The different algorithms crucially rely on the quantum speedup of the transient behavior of random walks