Related papers: Scalable Approximate Biclique Counting over Large …
Subgraph counting is a fundamental task for analyzing structural patterns in graph-structured data, with important applications in domains such as computational biology and social network analysis, where recurring motifs reveal functional…
Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter…
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…
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
Bipartite graphs are ubiquitous in many domains, e.g., e-commerce platforms, social networks, and academia, by modeling interactions between distinct entity sets. Within these graphs, the butterfly motif, a complete 2*2 biclique, represents…
We present a new approach for improving motif scanning accuracy, based on analysis of in-between similarity. Given a set of motifs obtained from a scanning process, we construct an associated weighted graph. We also compute the expected…
Dell, Lapinskas and Meeks [DLM SICOMP 2022] presented a general reduction from approximate counting to decision for a class of fine-grained problems that can be viewed as hyperedge counting or detection problems in an implicit hypergraph,…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We…
Single-source and top-$k$ SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these…
Given a bipartite graph $G = (V_1,V_2,E)$ where edges take on {\it both} positive and negative weights from set $\mathcal{S}$, the {\it maximum weighted edge biclique} problem, or $\mathcal{S}$-MWEB for short, asks to find a bipartite…
Exploratory analysis over network data is often limited by the ability to efficiently calculate graph statistics, which can provide a model-free understanding of the macroscopic properties of a network. We introduce a framework for…
Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are two computational approaches to count short cycles (with…
We investigate structural properties of the binary rank of Kronecker powers of binary matrices, equivalently, the biclique partition numbers of the corresponding bipartite graphs. To this end, we engineer a Column Generation approach to…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
We perform a detailed analysis of the C++ implementation of the Cluster Affiliation Model for Big Networks (BigClam) on the Stanford Network Analysis Project (SNAP). BigClam is a popular graph mining algorithm that is capable of finding…
We consider the problem of counting the copies of a length-$k$ pattern $\sigma$ in a sequence $f \colon [n] \to \mathbb{R}$, where a copy is a subset of indices $i_1 < \ldots < i_k \in [n]$ such that $f(i_j) < f(i_\ell)$ if and only if…
In the Flexible Graph Connectivity (FGC) problem, we are given an undirected multigraph on $n$ vertices with nonnegative edge costs, where each edge is classified as either safe or unsafe. Given integer parameters $p$ and $q$, the goal in…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…