相关论文: Parallel Batch-Dynamic $k$-Clique Counting

Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…

The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three…

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…

We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of $n$ nodes is vertex-partitioned among $k$ players that…

In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…

We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…

The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…

We develop the first theoretically-efficient algorithm for maintaining the maximal independent set (MIS) of a graph in the parallel batch-dynamic setting. In this setting, a graph is updated with batches of edge insertions/deletions, and…

Graph-cuts are widely used in computer vision. In order to speed up the optimization process and improve the scalability for large graphs, Strandmark and Kahl introduced a splitting method to split a graph into multiple subgraphs for…

We study the problem of counting the number of {\em isomorphic} copies of a given {\em template} graph, say $H$, in the input {\em base} graph, say $G$. In general, it is believed that polynomial time algorithms that solve this problem…

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…

Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent years, they have found significant applications in solvers for symmetric diagonally…

Emerging non-volatile main memory (NVRAM) technologies provide byte-addressability, low idle power, and improved memory-density, and are likely to be a key component in the future memory hierarchy. However, a critical challenge in achieving…

We consider the Euclidean $k$-means clustering problem in a dynamic setting, where we have to explicitly maintain a solution (a set of $k$ centers) $S \subseteq \mathbb{R}^d$ subject to point insertions/deletions in $\mathbb{R}^d$. We…

In this paper, we present an efficient massively parallel approximation algorithm for the $k$-means problem. Specifically, we provide an MPC algorithm that computes a constant-factor approximation to an arbitrary $k$-means instance in…

We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $\epsilon$-approximate packing and covering solvers which run in…

In fully dynamic clustering problems, a clustering of a given data set in a metric space must be maintained while it is modified through insertions and deletions of individual points. In this paper, we resolve the complexity of fully…

Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many…

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…

Single-linkage clustering is a popular form of hierarchical agglomerative clustering (HAC) where the distance between two clusters is defined as the minimum distance between any pair of points across the two clusters. In single-linkage HAC,…