Related papers: Linear-time uniform generation of random sparse co…
We present a randomized approximation algorithm for counting contingency tables, mxn non-negative integer matrices with given row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We define smooth margins (R,C) in terms of the…
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that $\Delta^4=O(m)$, where $\Delta$ is the maximal degree and $m$ is the number of edges,the algorithm runs in expected…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…
Let R=(r_1, ..., r_m) and C=(c_1, ..., c_n) be positive integer vectors such that r_1 +... + r_m=c_1 +... + c_n. We consider the set Sigma(R, C) of non-negative mxn integer matrices (contingency tables) with row sums R and column sums C as…
We represent the number of mxn non-negative integer matrices (contingency tables) with prescribed row sums and column sums as the expected value of the permanent of a non-negative random matrix with exponentially distributed entries. We…
We construct examples of contingency tables on $n$ binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…
The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this…
We consider nonnegative integer matrices with specified row and column sums and upper bounds on the entries. We show that the logarithm of the number of such matrices is approximated by a concave function of the row and column sums. We give…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
We present the first algorithm for generating random variates exactly uniformly from the set of perfect matchings of a bipartite graph with a polynomial expected running time over a nontrivial set of graphs. Previous Markov chain approaches…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of…
In high performance computing, scheduling of tasks and allocation to machines is very critical especially when we are dealing with heterogeneous execution costs. Simulations can be performed with a large variety of environments and…
Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an…