Related papers: Seeded Graph Matching via Large Neighborhood Stati…
Graph matching is a fruitful area in terms of both algorithms and theories. In this paper, we exploit the degree information, which was previously used only in noiseless graphs and perfectly-overlapping Erd\H{o}s--R\'enyi random graphs…
This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the…
Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem that has been extensively studied in recent years. We study a hypergraph version of the problem. Let $G^r(n,p)$ denote the…
In the \emph{graph matching} problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Dense subgraph discovery aims to find a dense component in edge-weighted graphs. This is a fundamental graph-mining task with a variety of applications and thus has received much attention recently. Although most existing methods assume…
Multiple methods of finding the vertices belonging to a planted dense subgraph in a random dense $G(n, p)$ graph have been proposed, with an emphasis on planted cliques. Such methods can identify the planted subgraph in polynomial time, but…
Let $f:\{-1,1\}^n$ be a polynomial with at most $s$ non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on $\{-1,1\}^n$ that runs in time polynomial in $n$ and…
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$…
We present several sparsification lower and upper bounds for classic problems in graph theory and logic. For the problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is no polynomial-time…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…
We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
We study distributed algorithms that find a maximal matching in an anonymous, edge-coloured graph. If the edges are properly coloured with $k$ colours, there is a trivial greedy algorithm that finds a maximal matching in $k-1$ synchronous…
We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks…