Related papers: Sparse graph counting and Kelley-Meka bounds for b…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…
A recent work of Abbasi et al. [FOCS 2023] introduced the notion of $\varepsilon$-scatter dimension of a metric space and showed a general framework for efficient parameterized approximation schemes (so-called EPASes) for a wide range of…
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…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
Given a set A in Z/NZ we may form a Cayley sum graph G_A on vertex set Z/NZ by joining i to j if and only if i + j is in A. We investigate the extent to which performing this construction with a random set A simulates the generation of a…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a…
We study the problem of counting the number of {\em isomorphic} copies of a given {\em template} graph, say $H$, in the input {\em base} graph, say $G$. In general, it is believed that polynomial time algorithms that solve this problem…
We present a simple greedy procedure to compute an $(\alpha,\beta)$-spanner for a graph $G$. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is…
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…
In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking…
We prove analogues for hypergraphs of Szemer\'edi's regularity lemma and the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemer\'edi theorem of Furstenberg and…
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs.…
An important question in extremal graph theory raised by Vera T. S\'os asks to determine for a given integer $t\ge 3$ and a given positive real number $\delta$ the asymptotically supremal edge density $f_t(\delta)$ that an $n$-vertex graph…
We study Ramsey properties of randomly perturbed $3$-uniform hypergraphs. For~$t\geq 2$, write $\tilde K^{(3)}_t$ to denote the $3$-uniform {\it expanded} clique hypergraph obtained from the complete graph $K_t$ by expanding each of the…
We determine new upper bounds for the clique numbers of strongly regular graphs in terms of their parameters. These bounds improve on the Delsarte bound for infinitely many feasible parameter tuples for strongly regular graphs, including…
This work proposes a framework LGKDE that learns kernel density estimation for graphs. The key challenge in graph density estimation lies in effectively capturing both structural patterns and semantic variations while maintaining…
Szemer\'edi's regularity lemma is a powerful tool in graph theory. It states that for every large enough graph, there exists a partition of the edge set with bounded size such that most induced subgraphs are quasirandom. When the graph is a…