Related papers: A Hybrid Sampling Scheme for Triangle Counting
We study the problem of approximating the $3$-profile of a large graph. $3$-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of a large graph. Our algorithm uses…
There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…
We study the problem of estimating the value of sums of the form $S_p \triangleq \sum \binom{x_i}{p}$ when one has the ability to sample $x_i \geq 0$ with probability proportional to its magnitude. When $p=2$, this problem is equivalent to…
The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…
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…
We consider the maximum matching problem in the semi-streaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a two-pass $(1/2 + 1/16)$-approximation…
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 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…
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…
Given an undirected graph $G=(V,E)$ on $n$ vertices, $m$ edges, and an integer $t\ge 1$, a subgraph $(V,E_S)$, $E_S\subseteq E$ is called a $t$-spanner if for any pair of vertices $u,v \in V$, the distance between them in the subgraph is at…
We consider the independent set problem in the semi-streaming model. For any input graph $G=(V, E)$ with $n$ vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, $G$ is…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…
We study four-cycle counting in arbitrary order graph streams. We present a 3-pass algorithm for $(1+\varepsilon)$-approximating the number of four-cycles using $\widetilde{O}(m/\sqrt{T})$ space, where $m$ is the number of edges and $T$ the…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
Large, distributed data streams are now ubiquitous. High-accuracy sketches with low memory overhead have become the de facto method for analyzing this data. For instance, if we wish to group data by some label and report the largest counts…
We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion. Specifically, we show that for any $\epsilon > 0$,…
Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a…
We study the maximum geometric independent set and clique problems in the streaming model. Given a collection of geometric objects arriving in an insertion only stream, the aim is to find a subset such that all objects in the subset are…
We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate…