Elimination of Algorithmic Branching in NP-Hard Scheduling via Multi-dimensional Semantic Geometric Processing

Abstract Combinatorial optimization problems, such as shift scheduling, are fundamentallyNP-Hard and are traditionally approached using algorithmic search trees (e.g.,backtracking, heuristic search, SAT solvers) that rely heavily on sequentialconditional branching. As the complexity of real-world constraints increases, thesealgorithms suffer from exponential combinatorial explosion, catastrophicdegradation of system maintainability, and immense computational overhead.Building upon the foundational data-layer architecture established in the previousMicroforce-Core research, this paper proposes a paradigm shift in the logic layer:representing discrete logical constraints not as algorithmic sequential conditions,but as continuous topological hyperplanes within a multi-dimensional state space.By executing bulk intersection operations (⋂) across these constraint manifolds,optimal solutions are extracted with O(1) logical depth, entirely bypassingconditional branching. Furthermore, we formalize the practical application of thistheory by mapping natural language constraints into the high-dimensionalsemantic vector spaces of Large Language Models (LLMs), executing deterministicgeometric intersections within probabilistic semantic domains.