Related papers: Towards a General Direct Product Testing Theorem
We study embeddings of graphs with bounded treewidth or bounded simple treewidth into the undirected graph underlying the directed product of two directed graphs. If the factors have bounded maximum indegrees, then the product graph has…
In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively…
Starting with a collection of traces generated by process executions, process discovery is the task of constructing a simple model that describes the process, where simplicity is often measured in terms of model size. The challenge of…
We show a direct product result for two-way public coin communication complexity of all relations in terms of a new complexity measure that we define. Our new measure is a generalization to non-product distributions of the two-way product…
We describe a $\tilde{O}(d^{5/6})$-query monotonicity tester for Boolean functions $f:[n]^d \to \{0,1\}$ on the $n$-hypergrid. This is the first $o(d)$ monotonicity tester with query complexity independent of $n$. Motivated by this…
We introduce DRESS, a deterministic, parameter-free framework that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging a non-linear…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
We obtain faster expander decomposition algorithms for directed graphs, matching the guarantees of Saranurak and Wang (SODA 2019) for expander decomposition on undirected graphs. Our algorithms are faster than prior work and also generalize…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
A set $D$ of vertices in a graph $G$ is called dominating if every vertex of $G$ is either in $D$ or adjacent to a vertex of $D$. The paired domination number $\gamma_{\mathrm{pr}}(G)$ of $G$ is the minimum size of a dominating set whose…
In this paper, we introduce a new graph structure, called the $direct~ sum ~graph$ on a finite dimensional vector space. We investigate the connectivity, diameter and the completeness of $\Gamma_{U\oplus W}(\mathbb{V})$. Further, we find…
A {\em product-injective labeling} of a graph $G$ is an injection $\chi: V(G) \to \mathbb{Z}$ such that $\chi(u)\chi(v) \not= \chi(x)\chi(y)$ for any distinct edges $uv, xy\in E(G)$. Let $P(G)$ be the smallest $N \geq 1$ such that there…
Given two vectors $u,v \in \mathbb{Q}^D$ over a finite domain $D$ and a function $f : D\times D\to D$, the convolution problem asks to compute the vector $w \in \mathbb{Q}^D$ whose entries are defined by $w(d) = \sum_{\substack{x,y \in D \\…
Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph models have been proposed to explain the macroscopic properties of these systems and to…
In this paper, the (infinite) direct product of fields is investigated. In particular, the finiteness of a given set is characterized in terms of some ring-theoretic observations. Next, a certain localization (whose multiplicative set…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…
We consider the problem of $L_p$-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. This class includes monotonicity, the Lipschitz property,…
We consider the problem of learning a set of direct causes of a target variable from an observational joint distribution. Learning directed acyclic graphs (DAGs) that represent the causal structure is a fundamental problem in science.…
This note provides a counterexample to a theorem announced in the last part of the paper ''Analysis of direct searches for discontinuous functions'', Mathematical Programming Vol. 133, pp.~299--325, 2012. The counterexample involves an…