Related papers: Sparse High Dimensional Expanders via Local Lifts
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
We study the problem of learning a hypergraph via edge detecting queries. In this problem, a learner queries subsets of vertices of a hidden hypergraph and observes whether these subsets contain an edge or not. In general, learning a…
Roadside vision centric 3D object detection has received increasing attention in recent years. It expands the perception range of autonomous vehicles, enhances the road safety. Previous methods focused on predicting per-pixel height rather…
We construct the first (locally computable, approximately) locally list decodable codes with rate, efficiency, and error tolerance approaching the information theoretic limit, a core regime of interest for the complexity theoretic task of…
This paper introduces novel relaxation hierarchies for concavo-convex programs (CXP), a class of problems that includes disjoint bilinear programming (DBP) and concave minimization (CM) as special cases. At the core of these hierarchies is…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current methods often fall short in capturing longer ranges, hierarchical structures, or community structures, which are common in various graphs…
We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of…
We illustrate the advantages of distance weighted discrimination for classification and feature extraction in a High Dimension Low Sample Size (HDLSS) situation. The HDLSS context is a gender classification problem of face images in which…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
In clinical applications, X-ray technology is vital for noninvasive examinations like mammography, providing essential anatomical information. However, the radiation risk associated with X-ray procedures raises concerns. X-ray…
State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cut refinement on each level of the hierarchy. Multilevel partitioners are…
Local complement is a graph operation formalized by Bouchet which replaces the neighborhood of a chosen vertex with its edge-complement. This operation induces an equivalence relation on graphs; determining the size of the resulting…
We construct an explicit family of 3-XOR instances hard for $\Omega(n)$-levels of the Sum-of-Squares (SoS) semi-definite programming hierarchy. Not only is this the first explicit construction to beat brute force search (beyond low-order…
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decomposition to the richer setting of hypermaps, naturally…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…
We show a new framework for constructing good distance lattices from high dimensional expanders. For error-correcting codes, which have a similar flavor as lattices, there is a known framework that yields good codes from expanders. However,…