The core theory presented is that Matrix Chain Multiplication optimization relies on the Principle of Optimality within Dynamic Programming: a global optimal solution can be constructed by combining solutions to subproblems, provided those sub-solutions are themselves locally optimal for their specific ranges. This mechanism formalizes the partitioning of matrix multiplication search spaces into disjoint subtrees defined by dimension arrays $d_0$ through $d_N$, where the computational cost is recursively minimized based on the number of scalar multiplications required ($p \times q \times r$). The concept belongs to Computational Complexity and Algorithm Design, specifically utilizing dynamic programming tables indexed by range boundaries to achieve polynomial time complexity ($O(n^3)$) rather than brute-force exponential search.
The core theory presented is that Matrix Chain Multiplication optimization relies on the Principle of Optimality within Dynamic Programming: a global optimal solution can be constructed by combining …