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Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…
We study the costs and benefits of different quantum approaches to finding approximate solutions of constrained combinatorial optimization problems with a focus on Maximum Independent Set. In the Lagrange multiplier approach we analyze the…
We address the Least Quantile of Squares (LQS) (and in particular the Least Median of Squares) regression problem using modern optimization methods. We propose a Mixed Integer Optimization (MIO) formulation of the LQS problem which allows…
Molecular docking is a critical computational method in drug discovery used to predict the binding conformation and orientation of a ligand within a protein's binding site. Mapping this challenge onto a graph-based problem, specifically the…
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and…
This paper studies the beamforming optimization challenge in reconfigurable intelligent surface (RIS)-aided multiple-input single-output (MISO) systems, where the RIS phase configuration is discrete. Conventional optimization methods for…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…
Recent advances in graph neural network architectures and increased computation power have revolutionized the field of combinatorial optimization (CO). Among the proposed models for CO problems, Neural Improvement (NI) models have been…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
The notion of {\em recoverable value} was advocated in work of Feige, Immorlica, Mirrokni and Nazerzadeh [Approx 2009] as a measure of quality for approximation algorithms. There this concept was applied to facility location problems. In…
We propose a fully differentiable architecture for simultaneous semantic and instance segmentation (a.k.a. panoptic segmentation) consisting of a convolutional neural network and an asymmetric multiway cut problem solver. The latter solves…
A general framework of unsupervised learning for combinatorial optimization (CO) is to train a neural network (NN) whose output gives a problem solution by directly optimizing the CO objective. Albeit with some advantages over traditional…
Graphs have been widely used to represent complex data in many applications. Efficient and effective analysis of graphs is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO)…
We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes…
Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted significant atten- tion since the sixties, when Wegner…
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…
In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) can exploit the causal…
The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search…