Related papers: Worst-Case to Expander-Case Reductions: Derandomiz…
A regular graph $G = (V,E)$ is an $(\varepsilon,\gamma)$ small-set expander if for any set of vertices of fractional size at most $\varepsilon$, at least $\gamma$ of the edges that are adjacent to it go outside. In this paper, we give a…
A $(\phi,\epsilon)$-expander-decomposition of a graph $G$ (with $n$ vertices and $m$ edges) is a partition of $V$ into clusters $V_1,\ldots,V_k$ with conductance $\Phi(G[V_i]) \ge \phi$, such that there are at most $\epsilon m$…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\delta \cdot…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
This paper presents significantly improved deterministic algorithms for some of the key problems in the area of distributed graph algorithms, including network decomposition, hitting sets, and spanners. As the main ingredient in these…
We consider the expander routing problem formulated by Ghaffari, Kuhn, and Su (PODC 2017), where the goal is to route all the tokens to their destinations given that each vertex is the source and the destination of at most $\deg(v)$ tokens.…
Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
Objective: Deformable image registration is a fundamental problem in medical image analysis, with applications such as longitudinal studies, population modeling, and atlas based image segmentation. Registration is often phrased as an…
Random subsampling of edges is a commonly employed technique in graph algorithms, underlying a vast array of modern algorithmic breakthroughs. Unfortunately, using this technique often leads to randomized algorithms with no clear path to…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
Derandomization techniques are often used within advanced randomized algorithms. In particular, pseudorandom objects, such as hash families and expander graphs, are key components of such algorithms, but their verification presents a…
The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…
In this paper, we consider a structural and geometric property of graphs, namely the presence of large expanders. The problem of finding such structures was first considered by Krivelevich [SIAM J. Disc. Math. 32 1 (2018)]. Here, we show…
This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…
The theme of this paper is how to find all instances of a given "sample" graph in a larger "data graph," using a single round of map-reduce. For the simplest sample graph, the triangle, we improve upon the best known such algorithm. We then…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…