Related papers: (Nearly) Efficient Algorithms for the Graph Matchi…
Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$…
In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…
Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set…
This paper studies the problem of recovering the hidden vertex correspondence between two correlated random graphs. We propose the partially correlated Erd\H{o}s-R\'enyi graphs model, wherein a pair of induced subgraphs with a certain…
We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we…
We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$ time on $n^{O(\log^2 n)}$ processors. The result is obtained by a derandomization of…
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…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
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 an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high…
We present a dynamic programming algorithm for optimally solving the Cograph Editing problem on an $n$-vertex graph that runs in $O(3^n n)$ time and uses $O(2^n)$ space. In this problem, we are given a graph $G = (V, E)$ and the task is to…
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…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is…