Related papers: Efficient Enumeration of Large Maximal k-Plexes
We present shared-memory parallel methods for Maximal Clique Enumeration (MCE) from a graph. MCE is a fundamental and well-studied graph analytics task, and is a widely used primitive for identifying dense structures in a graph. Due to its…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\tfrac12$. This random graph model is denoted…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we…
In this work, we consider the problem of sampling a $k$-clique in a graph from an almost uniform distribution in sublinear time in the general graph query model. Specifically the algorithm should output each $k$-clique with probability…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
Finding $k$-cores in graphs is a valuable and effective strategy for extracting dense regions of otherwise sparse graphs. We focus on the important problem of maintaining cores on rapidly changing dynamic graphs, where batches of edge…
The concept of $k$-defective clique, a relaxation of clique by allowing up-to $k$ missing edges, has been receiving increasing interests recently. Although the problem of finding the maximum $k$-defective clique is NP-hard, several…
Maximal biclique enumeration is a fundamental problem in bipartite graph data analysis. Existing biclique enumeration methods mainly focus on non-attributed bipartite graphs and also ignore the \emph{fairness} of graph attributes. In this…
A k-plex in a graph is a vertex set where each vertex is non-adjacent to at most k vertices (including itself) in this set, and the Maximum k-plex Problem (MKP) is to find the largest k-plex in the graph. As a practical NP-hard problem, MKP…
We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
This paper proposes efficient solutions for $k$-core decomposition with high parallelism. The problem of $k$-core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face…
We study the planted clique problem in which a clique of size k is planted in an Erdos-Renyi graph G(n,1/2) and one is interested in recovering this planted clique. It is widely believed that it exhibits a statistical-computational gap when…