相关论文: Faster Estimation of the Average Degree of a Graph…

A random graph order is a partial order achieved by independently sprinkling relations on a vertex set (each with probability $p$) and adding relations to satisfy the requirement of transitivity. A \textit{post} is an element in a partially…

For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…

Motivated by Hadwiger's conjecture, we study the problem of finding the densest possible $t$-vertex minor in graphs of average degree at least $t-1$. We show that if $G$ has average degree at least $t-1$, it contains a minor on $t$ vertices…

An independent transversal of a graph $G$ with a vertex partition $\mathcal P$ is an independent set of $G$ intersecting each block of $\mathcal P$ in a single vertex. Wanless and Wood proved that if each block of $\mathcal P$ has size at…

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…

We study the average performance of online greedy matching algorithms on $G(n,n,p)$, the random bipartite graph with $n$ vertices on each side and edges occurring independently with probability $p=p(n)$. In the online model, vertices on one…

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…

We consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this…

We consider the configuration model and the uniform simple graph with given degree sequence $\boldsymbol{d}=\left(d_i\right)_{i=1}^n$. We derive quantitative bounds for the errors in (i) joint normal-Poisson approximation to the numbers of…

The cut-rank of a set $X$ of vertices in a graph $G$ is defined as the rank of the $ X \times (V(G)\setminus X)$ matrix over the binary field whose $(i,j)$-entry is $1$ if the vertex $i$ in $X$ is adjacent to the vertex $j$ in…

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…

The densest subgraph of a large graph usually refers to some subgraph with the highest average degree, which has been extended to the family of $p$-means dense subgraph objectives by~\citet{veldt2021generalized}. The $p$-mean densest…

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…

Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time…

Let $G$ be a random graph on the vertex set $\{1,2,..., n\}$ such that edges in $G$ are determined by independent random indicator variables, while the probability $p_{ij}$ for $\{i,j\}$ being an edge in $G$ is not assumed to be equal.…

In this paper, we study Ranking, a well-known randomized greedy matching algorithm, for general graphs. The algorithm was originally introduced by Karp, Vazirani, and Vazirani [STOC 1990] for the online bipartite matching problem with…

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…

An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. When k = 1 the complexity of the problem is polynomial. In this paper, we further find the…

We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…