For any norms N_1,...,N_m on R^n and N(x):=N_1(x)+⋯+N_m(x), we show there is a
sparsified norm ̃N(x)=w_1N_1(x)+⋯+w_mN_m(x) such that |N(x)-̃N(x)|\leqslantεN(x) for all …

In a hypergraph on n vertices where D is the maximum size of a hyperedge, there is a
weighted hypergraph spectral-sparsifier with at most O (− 2 log (D)· n log n) hyperedges …

Given a matrix A∈ ℝ n× d, a partitioning of [n] into groups S 1,…, Sm, an outer norm p, and
inner norms such that either p≥ 1 and p 1,..., pm≥ 2 or p1=···= pm= p≥ 1/log d, we prove …

Graph sparsification has been an important topic with many structural and algorithmic
consequences. Recently hypergraph sparsification has come to the fore and has seen …

Spectral hypergraph sparsification, an attempt to extend well-known spectral graph
sparsification to hypergraphs, has been extensively studied over the past few years. For …

Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine
inequality, have been an important tool in both applied and pure mathematics. We study …

A (1±ϵ)-sparsifier of a hypergraph G(V,E) is a (weighted) subgraph that preserves the value
of every cut to within a (1±ϵ)-factor. It is known that every hypergraph with n vertices admits …

The splitting-off operation in undirected graphs is a fundamental reduction operation that
detaches all edges incident to a given vertex and adds new edges between the neighbors of …

We consider hypergraph network design problems where the goal is to construct a
hypergraph satisfying certain properties. In graph network design problems, the number of …

The $\ell_p $ subspace approximation problem is an NP-hard low rank approximation
problem that generalizes the median hyperplane problem ($ p= 1$), principal component …