Grow a tree on n vertices by starting with no edges and successively adding an edge chosen uniformly from the set of possible edges whose addition would not create a cycle. This process is closely related to the classical random graph process. We describe the asymptotic structure of the tree, as seen locally from a given vertex. In particular, we give an explicit expression for the asymptotic d...

Semi-device-independent quantum protocols realize information tasks – e.g. secure key distribution, random access coding, and randomness generation – in a scenario where no assumption on the internal working of the devices used in the protocol is made, except their dimension. These protocols offer two main advantages: first, their implementation is often less demanding than fully-device-indepen...

inventory models play an important role in determining the optimal ordering and pricing policies. much work has been reported in literature regarding inventory models with finite or infinite replenishment. but in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., hence, it is nee...

In recent years, a wealth of random graph models have arisen to explain the power-law degree distribution observed in the Internet [1] and other complex networks (see, for example, [6] and [8]). While power-law behavior often drives these models, less is known about other very natural properties found in complex networks. One such notion is the local versus global structure of a network. In [12...

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random k–regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the max...

We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so t...

We analyze the structure of random graphs generated by the geographical threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. We show how the degree distribution, percolation and connectivity transitions, clus...

We consider a generalized copy model of the web graph and related networks, and analyze its limiting behaviour. The model is motivated by previously proposed copying models of the web graph, where new nodes copy the link structure of existing nodes, and a certain number of additional random links are introduced. Our model parametrizes the number of random links, thereby allowing for the analysi...

We improve on a lattice algorithm of Tezuka for the computation of the k-distribution of a class of random number generators based on finite fields. We show how this is applied to the problem of constructing, for such generators, an output mapping yielding optimal k-distribution.