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Two of the most fundamental distributed symmetry-breaking problems are that of finding a maximal independent set (MIS) and a maximal matching (MM) in a graph. It is a major open question whether these problems can be solved in constant…
We study discrete random fields $\{X_t: t\in \mathbb{Z}^d\}$ parameterized on the $d$-dimensional integer lattice $\mathbb{Z}^d$. For a fixed threshold $u$, the excursion set $\{t \in \mathbb{Z}^d : X_t > u\}$ decomposes into connected…
This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial…
This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…
In the paper a piecewise constant image approximations of sequential number of pixel clusters or segments are treated. A majorizing of optimal approximation sequence by hierarchical sequence of image approximations is studied. Transition…
The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
Hypergraphs are a natural modeling paradigm for a wide range of complex relational systems. A standard analysis task is to identify clusters of closely related or densely interconnected nodes. Many graph algorithms for this task are based…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…
This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in…
We consider variants of the clustered planarity problem for level-planar drawings. So far, only convex clusters have been studied in this setting. We introduce two new variants that both insist on a level-planar drawing of the input graph…
The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…