As decentralized computing scenarios get ever more popular, unstructured topologies are natural candidates to consider running mix networks upon. We consider mix network topologies where mixes are placed on the nodes of an unstructured network, such as social networks and scale-free random networks. We explore the efficiency and traffic analysis resistance properties of mix networks based on un...

We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n−α and α = α(n) is bounded away from 0. We show that a.a.s. the resulting graph has a connected component of size n− o(n) which is an expander, and all other components are trees of bounded size. Sharper results are obt...

Recent research in statisticaland examplebased machine translation integrates ruleinduced structured representations with statistics and lexicalised exceptions. While rulebased approaches concentrate on the formation of partial translation hypotheses, probabilistic approaches are concerned with the evaluation and selection of the best hypotheses. Within the METIS-II framework, we propose a mach...

It is shown that there exists a sequence of 3-regular graphs {Gn}n=1 and a Hadamard space X such that {Gn}n=1 forms an expander sequence with respect to X, yet random regular graphs are not expanders with respect to X. This answers a question of [NS11]. {Gn}n=1 are also shown to be expanders with respect to random regular graphs, yielding a deterministic sublinear time constant factor approxima...

Let G = 〈S〉 be a solvable permutation group given as input by the generating set S. I.e. G is a solvable subgroup of the symmetric group Sn. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size Õ(n2) for G. More precisely, given a λ < 1, we can compute a subset T ⊂ G of size Õ(n2) ( 1 λ )O(1) such that the undirected Cayley graph Cay(G,T ) is a λ-s...

A k-lift of an n-vertex base-graph G is a graph H on n× k vertices, where each vertex of G is replaced by k vertices and each edge (u, v) in G is replaced by a matching representing a bijection πuv so that the edges of H are of the form ( (u, i), (v, πuv(i)) ) . H is a (uniformly) random lift of G if for every edge (u, v) the bijection πuv is chosen uniformly and independently at random. The ma...

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing. This paper considers the same problem with the added twist that the sparse coefficients of the unknown vector exhibit further correlations as determined by a k...

The randomized result was obtained by viewing random bit sequences as vertices of an expander graph and performing a random walk upon choosing a start vertex uniformly at random, and casting a majority vote. The error (probability of majority vote resulting in error) exponentially decreases with the length of the random walk. We also saw a stronger statement based on Chernoff bounds for random ...

Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional simplicial complexes, which are the high dimensional analogues of graphs, calls for the natural generalization of random walks to higher dimensions. In particu...

We show the existence of various versions of expander graphs using Kolmogorov complexity. This method seems superior to the usual “probabilistic construction”. Also, the best known bounds on the size of expanders and superconcentrators can be obtained this way. In the case of (acyclic) superconcentrators we obtain the density 34. Also, we review related graph properties, like magnification, edg...