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The minimum cost multicut problem is the NP-hard/APX-hard combinatorial optimization problem of partitioning a real-valued edge-weighted graph such as to minimize the total cost of the partition. While graph convolutional neural networks…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…

In Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is…

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…

Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…

Graph Neural Networks (GNNs) are key tools for graph representation learning, demonstrating strong results across diverse prediction tasks. In this paper, we present Convexified Message-Passing Graph Neural Networks (CGNNs), a novel and…

Resource allocation problems are often approached with linear programming techniques. But many concrete allocation problems in the experimental and observational sciences cannot or should not be expressed in the form of linear objective…

Graph Neural Networks (GNNs) have been extensively used for mining graph-structured data with impressive performance. However, because these traditional GNNs do not distinguish among various downstream tasks, embeddings embedded by them are…

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…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

Graph Neural Networks (GNNs) are the first choice for learning algorithms on graph data. GNNs promise to integrate (i) node features as well as (ii) edge information in an end-to-end learning algorithm. How does this promise work out…

Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with…

In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…

Graph neural networks (GNNs) have emerged as a promising solution to deal with unstructured data, outperforming traditional deep learning architectures. However, most of the current GNN models are designed to work with a single graph, which…

Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…