Related papers: Corrigendum: Sampling regular graphs and a peer-to…
We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is…
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…
We consider tilings of $\mathbb{Z}^2$ by two types of squares. We are interested in the rate of convergence to the stationarity of a natural Markov chain defined for square tilings. The rate of convergence can be represented by the mixing…
We survey existing techniques to bound the mixing time of Markov chains. The mixing time is related to a geometric parameter called conductance which is a measure of edge-expansion. Bounds on conductance are typically obtained by a…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
This paper explores the mixing time of the random transposition walk on the symmetric group. While it has long been known that this walk mixes in order n*log(n) time, this result has not previously been attained using coupling. A coupling…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
In earlier work, we showed that it is possible to achieve $O(\log N)$ streaming delay with high probability in a peer-to-peer network, where each peer has as little as four neighbors, while achieving any arbitrary fraction of the maximum…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
In this paper, we extend the classical Color Refinement algorithm for static networks to temporal (undirected and directed) networks. This enables us to design an algorithm to sample synthetic networks that preserves the $d$-hop…
We prove that whenever $d=d(n)\to\infty$ and $n-d\to\infty$ as $n\to\infty$, then with high probability for any non-trivial initial colouring, the colour refinement algorithm distinguishes all vertices of the random regular graph…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Graph dynamics arise naturally in many contexts. For instance in peer-to-peer networks, a participating peer may replace an existing connection with one neighbour by a new connection with a neighbour's neighbour. Several such local rewiring…
In this paper we study the mixing time of a biased transpositions shuffle on a set of $N$ cards with $N/2$ cards of two types. For a parameter $0<a \le 1$, one type of card is chosen to transpose with a bias of $\frac{a}{N}$ and the other…
It is often possible to speed up the mixing of a Markov chain $\{ X_{t} \}_{t \in \mathbb{N}}$ on a state space $\Omega$ by \textit{lifting}, that is, running a more efficient Markov chain $\{ \hat{X}_{t} \}_{t \in \mathbb{N}}$ on a larger…