Related papers: Efficient Algorithms for Attributed Graph Alignmen…
Structured prediction can be thought of as a simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise and unary potentials. The above is…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
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…
We give a first polynomial-time algorithm for (Weighted) Feedback Vertex Set on graphs of bounded maximum induced matching width (mim-width). Explicitly, given a branch decomposition of mim-width $w$, we give an $n^{\mathcal{O}(w)}$-time…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
Finding vertex-to-vertex correspondences in real-world graphs is a challenging task with applications in a wide variety of domains. Structural matching based on graphs connectivities has attracted considerable attention, while the…
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…
We consider the maximum vertex-weighted matching problem (MVM) for non-bipartite graphs. In earlier work we have described a 2/3-approximation algorithm for the MVM on bipartite graphs (Dobrian, Halappanavar, Pothen and Al-Herz, SIAM J.…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
Given an integer $k$ and a graph where every edge is colored either red or blue, the goal of the exact matching problem is to find a perfect matching with the property that exactly $k$ of its edges are red. Soon after Papadimitriou and…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
With the advent of end-to-end deep learning approaches in machine translation, interest in word alignments initially decreased; however, they have again become a focus of research more recently. Alignments are useful for typological…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…