Related papers: Sequential Algorithms and Independent Sets Discove…
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, {\L}acki,…
This work addresses the problem of exploration in an unknown environment. For linear dynamical systems, we use an experimental design framework and introduce an online greedy policy where the control maximizes the information of the next…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (i) continuum scaling limits of uniform simple connected graphs with given…
An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or…
The greedy sequential algorithm for maximal independent set (MIS) loops over the vertices in arbitrary order adding a vertex to the resulting set if and only if no previous neighboring vertex has been added. In this loop, as in many…
We investigate the number of maximal cliques, i.e., cliques that are not contained in any larger clique, in three network models: Erd\H{o}s-R\'enyi random graphs, inhomogeneous random graphs (also called Chung-Lu graphs), and geometric…
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformly at random from such a graph has expected…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
We give deterministic distributed $(1+\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\frac{1}{\epsilon} \log n)$ rounds,…
We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of…
Inductive $k$-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced $c$-colorable…
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
As standardly implemented in R or the Tetrad program, causal search algorithms used most widely or effectively by scientists have severe dimensionality constraints that make them inappropriate for big data problems without sacrificing…
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers…