Related papers: Why do simple algorithms for triangle enumeration …
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…
A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k>2, our algorithms for…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used…
Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation…
(I) We revisit the algorithmic problem of finding all triangles in a graph $G=(V,E)$ with $n$ vertices and $m$ edges. According to a result of Chiba and Nishizeki (1985), this task can be achieved by a combinatorial algorithm running in…
Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…
A $k$-truss is an edge-induced subgraph $H$ such that each of its edges belongs to at least $k-2$ triangles of $H$. This notion has been introduced around ten years ago in social network analysis and security, as a form of cohesive subgraph…
The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic,…
Triangle counting is a fundamental problem in the analysis of large graphs. There is a rich body of work on this problem, in varying streaming and distributed models, yet all these algorithms require reading the whole input graph. In many…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…
We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {\em…
Classically, planning tasks are studied as a two-step process: plan creation and plan execution. In situations where plan creation is slow (for example, due to expensive information access or complex constraints), a natural speed-up tactic…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded…
Triangle Counting (TC) is a procedure that involves enumerating the number of triangles within a graph. It has important applications in numerous fields, such as social or biological network analysis and network security. TC is a…