Related papers: REPT: A Streaming Algorithm of Approximating Globa…
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…
Triangle counting is a fundamental graph analytic operation that is used extensively in network science and graph mining. As the size of the graphs that needs to be analyzed continues to grow, there is a requirement in developing scalable…
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…
In this work, we present the first efficient and practical algorithm for estimating the number of triangles in a graph stream using predictions. Our algorithm combines waiting room sampling and reservoir sampling with a predictor for the…
Listing and counting triangles in graphs is a key algorithmic kernel for network analyses, including community detection, clustering coefficients, k-trusses, and triangle centrality. In this paper, we propose the novel concept of a…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
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…
The problem of (approximately) counting the number of triangles in a graph is one of the basic problems in graph theory. In this paper we study the problem in the streaming model. We study the amount of memory required by a randomized…
We implement exact triangle counting in graphs on the GPU using three different methodologies: subgraph matching to a triangle pattern; programmable graph analytics, with a set-intersection approach; and a matrix formulation based on sparse…
Triangle counting is a fundamental technique in network analysis, that has received much attention in various input models. The vast majority of triangle counting algorithms are targeted to static graphs. Yet, many real-world graphs are…
We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {\em…
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,…
We present a new algorithm for approximating the number of triangles in a graph $G$ whose edges arrive as an arbitrary order stream. If $m$ is the number of edges in $G$, $T$ the number of triangles, $\Delta_E$ the maximum number of…
Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
Finding the number of triangles in a network is an important problem in the analysis of complex networks. The number of triangles also has important applications in data mining. Existing distributed memory parallel algorithms for counting…
The number of triangles (hereafter denoted by $\Delta$) is an important metric to analyze massive graphs. It is also used to compute clustering coefficient in networks. This paper proposes a new algorithm called PES (Priority Edge Sampling)…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph $G$, one can query the degree of a vertex, the existence of an edge between…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…