Related papers: A Cycle Walk for Sampling Measures on Spanning For…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…
We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…
A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…
Quantum walks on graphs have been shown in certain cases to mix quadratically faster than their classical counterparts. Lifted Markov chains, consisting of a Markov chain on an extended state space which is projected back down to the…
We present a Markov chain (Dikin walk) for sampling from a convex body equipped with a self-concordant barrier, whose mixing time from a "central point" is strongly polynomial in the description of the convex set. The mixing time of this…
Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by…
Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler and random walk Metropolis algorithm are…
The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T.…
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…
We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of…
We give qualitative and quantitative improvements to theorems which enable significance testing in Markov Chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political…
Gerrymandering is the perversion of an election based on manipulation of voting district boundaries, and has been a historically important yet difficult task to analytically prove. We propose a Markov Chain Monte Carlo with Simulated…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…
Graph labelling is a key activity of network science, with broad practical applications, and close relations to other network science tasks, such as community detection and clustering. While a large body of work exists on both unsupervised…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…