相关论文: Low-degree Security of the Planted Random Subgraph…

Given a large data matrix $A\in\mathbb{R}^{n\times n}$, we consider the problem of determining whether its entries are i.i.d. with some known marginal distribution $A_{ij}\sim P_0$, or instead $A$ contains a principal submatrix $A_{{\sf…

In this paper, matching pairs of stocahstically generated graphs in the presence of generalized seed side-information is considered. The graph matching problem emerges naturally in various applications such as social network…

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the…

Dense subgraph discovery is a fundamental problem in graph mining with a wide range of applications \cite{gionis2015dense}. Despite a large number of applications ranging from computational neuroscience to social network analysis, that take…

Denote by $A$ the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing $\langle A-E\{A\},X\rangle$ over the set of positive semidefinite matrices $X$ with diagonal entries $X_{ii}=1$.…

Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted…

We consider the problem of inferring a matching hidden in a weighted random $k$-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to…

A bipartite graph $G=(L,R;E)$ with at least one edge is said to be identifiable if for every vertex $v\in L$, the subgraph induced by its non-neighbors has a matching of cardinality $|L|-1$. An $\ell$-subgraph of $G$ is an induced subgraph…

In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…

We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset…

We provide a new provably-secure steganographic encryption protocol that is proven secure in the complexity-theoretic framework of Hopper et al. The fundamental building block of our steganographic encryption protocol is a "one-time…

LLM-powered search services have driven data integration as a significant trend. However, this trend's progress is fundamentally hindered, despite the fact that combining individual knowledge can significantly improve the relevance and…

Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…

A new, constructive proof with a small explicit constant is given to the Erd\H{o}s-Pyber theorem which says that the edges of a graph on $n$ vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at…

We give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns…

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on…

We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random…

Resolving a conjecture of F\"uredi from 1988, we prove that with high probability, the random graph $G(n,1/2)$ admits a friendly bisection of its vertex set, i.e., a partition of its vertex set into two parts whose sizes differ by at most…

We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…