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Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization.…

Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the…

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…

The recent work ``Combinatorial Optimization with Physics-Inspired Graph Neural Networks'' [Nat Mach Intell 4 (2022) 367] introduces a physics-inspired unsupervised Graph Neural Network (GNN) to solve combinatorial optimization problems on…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…

In this paper, we propose a novel graph-based approach for semi-supervised learning problems, which considers an adaptive adjacency of the examples throughout the unsupervised portion of the training. Adjacency of the examples is inferred…

Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard combinatorial optimization problems in the form of binary variables. The Hamiltonian function is often used to formulate QUBO problems where…

Combinatorial Optimization (CO) problems over graphs appear routinely in many applications such as in optimizing traffic, viral marketing in social networks, and matching for job allocation. Due to their combinatorial nature, these problems…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…

We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the…

We present the first unsupervised learning model for Maximum-Independent-Set (MaxIS) in dynamic graphs where edges change over time. Our method combines structural learning from graph neural networks (GNNs) with a learned distributed update…

We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various…

Although graph neural networks (GNNs) have achieved impressive achievements in graph classification, they often need abundant task-specific labels, which could be extensively costly to acquire. A credible solution is to explore additional…

Combinatorial optimization (CO) on graphs is a classic topic that has been extensively studied across many scientific and industrial fields. Recently, solving CO problems on graphs through learning methods has attracted great attention.…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…