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Algorithms for large and evolving graphs operate under different constraints: updates must be processed quickly, only a small fraction of the input may be inspected, or computation must rely on local information. These requirements motivate distinct computational models, yet the algorithmic ideas that succeed in them are often closely related.
The talk explores examples of these connections through recent advances in graph matching, including my own work on dynamic and sublinear algorithms. Building on these examples, I will outline a broader research direction: developing algorithmic paradigms that admit efficient implementations across computational models, and understanding how extremal combinatorial structures shape their complexity.