Related papers: Testing Graph Clusterability: Algorithms and Lower…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
In the Partially Embedded Planarity problem, we are given a graph $G$ together with a topological drawing of a subgraph $H$ of $G$. The task is to decide whether the drawing can be extended to a drawing of the whole graph such that no two…
We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing…
We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…
Higher-order graph clustering aims to partition the graph using frequently occurring subgraphs. Motif conductance is one of the most promising higher-order graph clustering models due to its strong interpretability. However, existing motif…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
The main problem in the area of graph property testing is to understand which graph properties are \emph{testable}, which means that with constantly many queries to any input graph $G$, a tester can decide with good probability whether $G$…
In the subgraph counting problem, we are given a input graph $G(V, E)$ and a target graph $H$; the goal is to estimate the number of occurrences of $H$ in $G$. Our focus here is on designing sublinear-time algorithms for approximately…
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. More precisely, we show that a graph having modularity…
Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
Modularity clustering is an essential tool to understand complicated graphs. However, existing methods are not applicable to massive graphs due to two serious weaknesses. (1) It is difficult to fully reproduce ground-truth clusters due to…
We propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the…
The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…
Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$). We give an…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…