相关论文: Testability and local certification of monotone pr…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
This paper studies algorithmic meta theorems for property testing with \emph{constant running time} in the bounded degree model. In (Adler, Harwath 2018) it was shown that on graph classes $\mathcal C^{w}_d$ consisting of all graphs with…
A class of graphs is structurally nowhere dense if it can be constructed from a nowhere dense class by a first-order transduction. Structurally nowhere dense classes vastly generalize nowhere dense classes and constitute important examples…
A graph property P is strongly testable if for every fixed \epsilon>0 there is a one-sided \epsilon-tester for P whose query complexity is bounded by a function of \epsilon. In classifying the strongly testable graph properties, the first…
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…
We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
We provide a combinatorial characterization of all testable properties of $k$-uniform hypergraphs ($k$-graphs for short). Here, a $k$-graph property $P$ is testable if there is a randomized algorithm which makes a bounded number of edge…
For studying topological obstructions to graph colorings, Hom-complexes were introduced by Lov\'{a}sz. A graph $T$ is called a test graph if for every graph $H$, the $k$-connectedness of $|Hom(T, H)|$ implies $\chi (H)\geq k + 1 + \chi(T)$.…
Stability and dependence are model-theoretic notions that have recently proved highly effective in the study of structural and algorithmic properties of hereditary graph classes, and are considered key notions for generalizing to hereditary…
We study the problems of counting copies and induced copies of a small pattern graph $H$ in a large host graph $G$. Recent work fully classified the complexity of those problems according to structural restrictions on the patterns $H$. In…
Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…
For a graph $G$ and $t,k\in\mathbb{Z}^+$ a \emph{$t$-tone $k$-coloring} of $G$ is a function $f:V(G)\rightarrow \binom{[k]}{t}$ such that $|f(v)\cap f(w)| < d(v,w)$ for all distinct $v,w \in V(G)$. The \emph{$t$-tone chromatic number} of…
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
It is known that for subgraph-closed graph classes the first-order model checking problem is fixed-parameter tractable if and only if the class is nowhere dense [Grohe, Kreutzer, Siebertz, STOC 2014]. However, the dependency on the formula…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
Given a graph property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ asks, on input a graph $G$ and a positive integer $k$, to compute the number of induced subgraphs of size $k$ in $G$ that satisfy $\Phi$. The search for explicit criteria…
We study property testing in directed graphs in the bounded degree model, where we assume that an algorithm may only query the outgoing edges of a vertex, a model proposed by Bender and Ron in 2002. As our first main result, we we present a…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$). We give an…