Related papers: Graph Matching: Relax at Your Own Risk
In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise…
Machine learning and data mining algorithms have been increasingly used recently to support decision-making systems in many areas of high societal importance such as healthcare, education, or security. While being very efficient in their…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a…
Graph matching is one of the most significant graph analytic tasks, which aims to find the node correspondence across different graphs. Most existing graph matching approaches mainly rely on topological information, whose performances are…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
We contribute to approximate algorithms for the quadratic assignment problem also known as graph matching. Inspired by the success of the fusion moves technique developed for multilabel discrete Markov random fields, we investigate its…
A matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a $b$-matching every vertex $v$ has an associated bound $b_v$, and a maximum $b$-matching is a…
We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…