(371as) Modular Forms in Combinatorial Optimization

From strategizing a game of chess to optimizing agrivoltaics, we encounter combinatorial optimization in various domains. Despite its widespread application, our understanding of the problem's underlying structure remains limited, thereby, constraining our ability to develop algorithms that can efficiently solve these problems.

In this paper, we prove and explore the intrinsic modular nature of combinatorial optimization problems. By gaining insights into the structural form, we can develop sophisticated algorithms to solve these problems. Specifically, we explore this modular structure's implications for both unconstrained and constrained solutions of the Asymmetric Traveling Salesman Problem (ATSP).