相关论文: Uniform random sampling of planar graphs in linear…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
This paper introduces an innovative and intuitive finite population sampling method that has been developed using a unique graphical framework. In this approach, first-order inclusion probabilities are represented as bars on a…
We present three simple algorithms to uniformly generate `Fibonacci words' (i.e., some words that are enumerated by Fibonacci numbers), Schr{\"o}der trees of size $n$ and Motzkin left factors of size $n$ and final height $h$. These…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…
We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are…
Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical…
In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…
We prove algorithmic weak and \Szemeredi{} regularity lemmas for several classes of sparse graphs in the literature, for which only weak regularity lemmas were previously known. These include core-dense graphs, low threshold rank graphs,…
By introducing a subsampling strategy, we propose a randomized block Kaczmarz-Motzkin method for solving linear systems. Such strategy not only determines the block size, but also combines and extends two famous strategies, i.e., randomness…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
Boson sampling is a key candidate for demonstrating quantum advantage, and has already yielded significant advances in quantum simulation, machine learning, and graph theory. In this work, a unification and extension of distinct forms of…
In this paper, we consider a randomized greedy algorithm for independent sets in $r$-uniform $d$-regular hypergraphs $G$ on $n$ vertices with girth $g$. By analyzing the expected size of the independent sets generated by this algorithm, we…
We propose a novel exact algorithm for generating connected Erdos-Renyi random graphs $G(n,p)$. The method couples the graph exploration process to an inhomogeneous Poisson random walk, which yields an exact sampler that runs in $O(n)$ time…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…