相关论文: Power-Law Graph Cuts

Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure…

A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…

Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…

An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

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 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…

The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…

Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain…

We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random…

Many large datasets exhibit power-law statistics: The web graph, social networks, text data, click through data etc. Their adjacency graphs are termed natural graphs, and are known to be difficult to partition. As a consequence most…

The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this…

Vertex-level clustering for directed graphs (digraphs) remains challenging as edge directionality breaks the key assumptions underlying popular spectral methods, which also incur the overhead of eigen-decomposition. This paper proposes…

We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…

This paper presents a framework that supports the implementation of parallel solutions for the widespread parametric maximum flow computational routines used in image segmentation algorithms. The framework is based on supergraphs, a special…

Graph Spectral Clustering methods (GSC) allow representing clusters of diverse shapes, densities, etc. However, the results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…