Related papers: Direct sampling of short paths for contiguous part…
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
This work focuses on the quantum mixing time, which is crucial for efficient quantum sampling and algorithm performance. We extend Richter's previous analysis of continuous time quantum walks on the periodic lattice $\mathbb{Z}_{n_1}\times…
In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with sub-exponential…
We show that a circuit walk from a given feasible point of a given linear program to an optimal point can be computed in polynomial time using only linear algebra operations and the solution of the single given linear program. We also show…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
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…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the…
Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…