Related papers: The Complexity of Three-Way Statistical Tables
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors.…
The three-way table problem is to decide if there exists an l x m x n table satisfying given line sums, and find a table if there is one. It is NP-complete already for l=3 and every bounded integer program can be isomorphically represented…
Deciding the existence of an $l\times m\times n$ integer threeway table with given line-sums is NP-complete already for fixed $l=3$, but is in P with both $l,m$ fixed. Here we consider {\em huge} tables, where the variable dimension $n$ is…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…
Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…
A result of Deza, Levin, Meesum, and Onn shows that the problem of deciding if a given sequence is the degree sequence of a 3-uniform hypergraph is NP complete. We tackle this problem in the random case and show that a random integer…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
We consider the problem of statistical inference on unknown quantities structured as a multiway table. We show that such multiway tables are naturally formed by arranging regression coefficients in complex systems of linear models for…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…
This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…
We introduce a variant of the multiway cut that we call the min-max connected multiway cut. Given a graph $G=(V,E)$ and a set $\Gamma\subseteq V$ of $t$ terminals, partition $V$ into $t$ parts such that each part is connected and contains…
A theory of numerical path-following in toric varieties was suggested in two previous papers. The motivation is solving systems of polynomials with real or complex coefficients. When those polynomials are not assumed 'dense', solving them…
We study a multi-marginal optimal transportation problem with a cost function of the form $c(x_{1}, \ldots,x_{m})=\sum_{k=1}^{m-1}|x_{k}-x_{k+1}|^{2} + |x_{m}- F(x_{1})|^{2}$, where $F: \mathbb{R}^n \rightarrow \mathbb{R}^n$. When $m=4$,…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
The paper derives new results on the marginal likelihood of a two-way table which clarify the conditions under which Ecological inference is possible and lead to an efficient algorithm for maximizing the exact multinomial likelihood. The…