Related papers: How the Degeneracy Helps for Triangle Counting in …
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 revisit the classic basic counting problem in the distributed streaming model that was studied by Gibbons and Tirthapura (GT). In the solution for maintaining an $(\epsilon,\delta)$-estimate, as what GT's method does, we make the…
We show that the VC-dimension of a graph can be computed in time $n^{\log d+1} d^{O(d)}$, where $d$ is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that…
We introduce the {\em certification} of solutions to graph problems when access to the input is restricted. This topic has received a lot of attention in the distributed computing setting, and we introduce it here in the context of…
Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
Given a $k$-node pattern graph $H$ and an $n$-node host graph $G$, the subgraph counting problem asks to compute the number of copies of $H$ in $G$. In this work we address the following question: can we count the copies of $H$ faster if…
A graph spanner is a fundamental graph structure that faithfully preserves the pairwise distances in the input graph up to a small multiplicative stretch. The common objective in the computation of spanners is to achieve the best-known…
We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify…
We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the…
We consider a basic problem in the general data streaming model, namely, to estimate a vector $f \in \Z^n$ that is arbitrarily updated (i.e., incremented or decremented) coordinate-wise. The estimate $\hat{f} \in \Z^n$ must satisfy…
Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like…
Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…
In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
Graphs are a fundamental data structure used to represent relationships in domains as diverse as the social sciences, bioinformatics, cybersecurity, the Internet, and more. One of the central observations in network science is that…
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…