Optimization-based approximation algorithms:

The seminar focuses on optimization-based approximation algorithms, essential tools for solving complex computational problems where exact solutions are impractical due to high complexity. It explores fundamental problems such as vertex cover and maxcut, analyzing their mathematical formulations and applications in networks, surveillance, and infrastructure design. The talk explains the difference between convex and integer optimization, highlighting the challenges of working with discrete problems and the need for approximate approaches that guarantee efficient solutions in polynomial time. It presents relaxation techniques and advanced heuristics, including the use of separation oracles in convex optimization and linear programming-based methods to enhance the accuracy of approximate solutions. The seminar also discusses the limits of these algorithms, quantifying their performance using approximation factors and exploring strategies to improve efficiency without sacrificing solution quality. It concludes with practical applications of these algorithms in optimizing complex systems, from network planning to data analysis in artificial intelligence. Current challenges in the design of new approximation strategies are emphasized, as well as the impact of these methods on computational theory and real-world problem-solving.