Related papers: Combinatorial Optimization with Physics-Inspired G…

We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…

The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…

To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…

Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such…

Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…

Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…

Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most…

One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…

Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…

Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that…

Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…

We provide a comprehensive reply to the comment written by Stefan Boettcher [arXiv:2210.00623] and argue that the comment singles out one particular non-representative example problem, entirely focusing on the maximum cut problem (MaxCut)…

Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…

Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…

Graph neural networks (GNNs) are a type of deep learning models that are trained on graphs and have been successfully applied in various domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to…