Related papers: Local Graph Clustering Beyond Cheeger's Inequality
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We introduce a new notion…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
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 propose the first \emph{local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean $k$-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1…
A {\em local graph partitioning algorithm} finds a set of vertices with small conductance (i.e. a sparse cut) by adaptively exploring part of a large graph $G$, starting from a specified vertex. For the algorithm to be local, its complexity…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic $O(m \log^2 n \log\log^2 n)$ time algorithm. This improves both on the best previously known deterministic running time of $O(m \log^{12}…
We provide a deterministic $\tilde{O}(\log N)$-space algorithm for estimating random walk probabilities on undirected graphs, and more generally Eulerian directed graphs, to within inverse polynomial additive error…
Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…
Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically…
Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that…
We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive $(+)$ or negative $(-)$, and the objective is to find a clustering that minimizes the…
In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on the message complexity. We provide an algorithm that solves the implicit version of leader election (where…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
We study the problem of finding a small sparse cut in an undirected graph. Given an undirected graph G=(V,E) and a parameter k <= |E|, the small sparsest cut problem is to find a subset of vertices S with minimum conductance among all sets…
In this paper, we make use of the Metropolis-type walks due to Nonaka et al. (2010) to provide a faster solution to the $S$-$T$-connectivity problem in undirected graphs (USTCON). As our main result, we propose a family of randomized…
Diffusions and related random walk procedures are of central importance in many areas of machine learning, data analysis, and applied mathematics. Because they spread mass agnostically at each step in an iterative manner, they can sometimes…
A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy…
In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent direction} has a favorable local behavior. In view of its global…