Related papers: Testable algorithms for approximately counting edg…
In this short note, we give a novel algorithm for $O(1)$ round triangle counting in bounded arboricity graphs. Counting triangles in $O(1)$ rounds (exactly) is listed as one of the interesting remaining open problems in the recent survey of…
Triangle counting is a fundamental and widely studied problem on static graphs, and recently on temporal graphs, where edges carry information on the timings of the associated events. Streaming processing and resource efficiency are crucial…
The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic,…
Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle…
We present a randomized algorithm that computes a constant approximation of a graph's arboricity, using $\tilde{O}(n/\lambda)$ queries to adjacency lists and in the same time bound. Here, $n$ and $\lambda$ denote the number of nodes and the…
The performance of graph algorithms is often measured in terms of the number of traversed edges per second (TEPS). However, this performance metric is inadequate for a graph operation such as exact triangle counting. In triangle counting,…
Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used…
We revisit the well-studied problem of triangle count estimation in graph streams. Given a graph represented as a stream of $m$ edges, our aim is to compute a $(1\pm\varepsilon)$-approximation to the triangle count $T$, using a small space…
Triangle counting is a fundamental problem in the analysis of large graphs. There is a rich body of work on this problem, in varying streaming and distributed models, yet all these algorithms require reading the whole input graph. In many…
We consider a weighted counting problem on matchings, denoted $\textrm{PrMatching}(\mathcal{G})$, on an arbitrary fixed graph family $\mathcal{G}$. The input consists of a graph $G\in \mathcal{G}$ and of rational probabilities of existence…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs,…
We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…
We design a space efficient algorithm that approximates the transitivity (global clustering coefficient) and total triangle count with only a single pass through a graph given as a stream of edges. Our procedure is based on the classic…
We consider the problem of counting straight-edge triangulations of a given set $P$ of $n$ points in the plane. Until very recently it was not known whether the exact number of triangulations of $P$ can be computed asymptotically faster…
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…
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…