Related papers: Graph powering and spectral robustness
We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker's approach gives a PTAS on planar graphs,…
We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search.…
The analytic connectivity, proposed as a substitute of the algebraic connectivity in the setting of hypergraphs, is an important quantity in spectral hypergraph theory. The definition of the analytic connectivity for a uniform hypergraph…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
We provide a method to obtain beyond-worst-case time complexity for any single-source-shortest-path (SSSP) algorithm by exploiting modular structures in graphs. The key novelty is a graph decomposition, called the acyclic-connected (A-C)…
In a recent breakthrough, Kelley and Meka (FOCS 2023) obtained a strong upper bound on the density of sets of integers without nontrivial three-term arithmetic progressions. In this work, we extend their result, establishing similar bounds…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
We introduce and develop a theory of limits for sequences of sparse graphs based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs…
A seminal palette sparsification result of Assadi, Chen, and Khanna states that in every $n$-vertex graph of maximum degree $\Delta$, sampling $\Theta(\log n)$ colors per vertex from $\{1, \ldots, \Delta+1\}$ almost certainly allows for a…
Community structure is an important property that captures inhomogeneities common in large networks, and modularity is one of the most widely used metrics for such community structure. In this paper, we introduce a principled methodology,…
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
Network sparsification is the task of reducing the number of edges of a given graph while preserving some crucial graph property. In community-aware network sparsification, the preserved property concerns the subgraphs that are induced by…
Several algorithmic meta-theorems on kernelization have appeared in the last years, starting with the result of Bodlaender et al. [FOCS 2009] on graphs of bounded genus, then generalized by Fomin et al. [SODA 2010] to graphs excluding a…
A geometric graph associated with a set of points $P= \{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$ and a fixed kernel function $\mathsf{K}:\mathbb{R}^d\times \mathbb{R}^d\to\mathbb{R}_{\geq 0}$ is a complete graph on $P$ such that the…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
The non-backtracking operator was recently shown to provide a significant improvement when used for spectral clustering of sparse networks. In this paper we analyze its spectral density on large random sparse graphs using a mapping to the…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…