Combinatorial Optimization Courses and Certifications

Hausdorff Center for Mathematics

Finding Perfect Matchings in Bipartite Hypergraphs

Explore efficient algorithms for finding perfect matchings in bipartite hypergraphs, extending Haxell's condition and the Hungarian algorithm to hypergraph structures.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Louis Theran: Rigidity of Random Graphs in Higher Dimensions

Explore rigidity properties of random graphs in higher dimensions and their connection to matrix completion, with insights on thresholds and optimal conditions.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Recent Results on Maximizing Submodular Functions

Explore recent advancements in submodular maximization, covering constrained and unconstrained scenarios for monotone and non-monotone functions within combinatorial optimization.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Provable Submodular Function Minimization via Fujishige Wolfe Algorithm

Explore submodular function minimization through the Fujishige-Wolfe algorithm, analyzing its convergence and implications for combinatorial optimization.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Maximizing Monotone Submodular Functions over the Integer Lattice

Explore advanced algorithms for maximizing monotone submodular functions on integer lattices, with applications in machine learning and combinatorial optimization.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Reassembling Trees for the Traveling Salesman

Explore advanced approximation algorithms for traveling salesman problems, focusing on tree reassembly techniques to improve solutions beyond traditional methods.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On Element Connectivity Preserving Graph Simplification

Explores element-connectivity in graph simplification, focusing on reduction techniques, algorithmic results, and applications in network design. Highlights open problems and submodularity properties for faster algorithms.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Neil Olver: On the Integrality Gap of the Prize Collecting Steiner Forest LP

Explores the integrality gap of the prize collecting Steiner forest LP, disproving the belief it was 2 and showing it's at least 9/4, with implications for approximation algorithms in combinatorial optimization.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Viswanath Nagarajan - Stochastic Load Balancing on Unrelated Machines

Explores stochastic load balancing on unrelated machines, presenting a constant factor approximation algorithm for minimizing expected makespan. Discusses LP relaxation and rounding techniques.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Deep Learning for Combinatorial Optimization - Count Your Flops & Make Your Flops Count

Explores deep learning for combinatorial optimization, focusing on reducing computation through learned models while balancing solution quality. Discusses practical examples, challenges, and future research directions.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

How Much Data Is Sufficient to Learn High-Performing Algorithms?

Explore data-driven algorithm design's impact on performance, focusing on generalization guarantees for combinatorial algorithms with piecewise-structured parameter functions.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

A Framework for Differentiable Discovery of Graph Algorithms

Explore graph algorithm discovery using deep learning and tree decomposition. Learn effective techniques for NP-complete problems with interpretable results and expanded search space.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Polyhedral Techniques in Combinatorial Optimization - Matchings and Tours

Explore recent advancements in combinatorial optimization, focusing on matching and traveling salesman problems. Learn about polyhedral techniques and linear programming formulations for designing efficient algorithms.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Formalising the Theory of Combinatorial Optimisation

Explore formalisation of combinatorial optimisation theory in Isabelle/HOL, focusing on matching theory and its mathematical implications for computer science and applied mathematics.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Southeast University

组合最优化

Master combinatorial optimization theory and algorithms, from linear programming to integer programming, covering flows, matchings, matroids and cutting-plane methods through practical examples and applications.

• XuetangX
• On-Demand
• Free Online Course