When and Why Do Efficient Algorithms Exist for Constraint Satisfaction and Beyond

Explore the fundamental principles behind efficient algorithms in computational problem-solving through this insightful lecture by Venkatesan Guruswami at #ICBS2024. Delve into the diverse landscape of computational problems, examining the mathematical structures that lead to efficient solutions or dictate intractability. Discover the algebraic dichotomy theorem in constraint satisfaction problems, which provides a definitive answer to when polynomial-time algorithms exist. Investigate the concept of polymorphisms and their role in determining problem complexity. Examine potential extensions of the polymorphic principle beyond constraint satisfaction problems and its implications for fine-grained complexity, optimization, and algorithmic techniques. Gain a deeper understanding of the classification of computational complexity, a core focus in theoretical computer science.