Related papers: (Nearly) Efficient Algorithms for the Graph Matchi…
In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation…
We investigate contextual graph matching in the Gaussian setting, where both edge weights and node features are correlated across two networks. We derive precise information-theoretic thresholds for exact recovery, and identify conditions…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition…
Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the…
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 develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…
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 investigate the existence of a statistical-computational gap in multiple Gaussian graph alignment. We first generalize a previously established informational threshold from Vassaux and Massouli\'e (2025) to regimes where the number of…
We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset Intersection (CI) can be solved in quasipolynomial ($\exp((\log n)^{O(1)})$) time. The best previous bound…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
We give an algorithm that, given graphs $G$ and $H$, tests whether $H$ is a minor of $G$ in time ${\cal O}_H(n^{1+o(1)})$; here, $n$ is the number of vertices of $G$ and the ${\cal O}_H(\cdot)$-notation hides factors that depend on $H$ and…
We present an algorithm that takes as input an $n$-vertex planar graph $G$ and a $k$-vertex pattern graph $P$, and computes the number of (induced) copies of $P$ in $G$ in $2^{O(k/\log k)}n^{O(1)}$ time. If $P$ is a matching, independent…
This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Their fundamental result…
In a recent breakthrough, Babai (STOC 2016) gave a quasipolynomial time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithms runs in time $n^{O((\log d)^{c})}$, where $n$ is…