Combinatorial Aspect of Code Restructuring for Virtual Memory Computer Systems Under WS Swapping Strategy.

This paper presents innovative findings on the restructuring of code for virtual memory systems operating under a working set swapping strategy. Despite extensive research spanning five decades and numerous studies dedicated to restructuring, the persisting absence of definitive solutions has motivated this inquiry. The NP-hard problem of code block relocation across virtual memory pages to minimize cost function reflects a core challenge inherent to the problem. For ill-defined programs, many practical cluster-based solutions lack a quantifiable approximation error to the unknown optimal or ε-optimal solution. This paper elucidates the computational process by offering a geometric interpretation, enabling the construction of a combinatorial mathematical model of the restructuring process. This model incorporates both functional elements and constraints to define acceptable solutions. The unique aspects of the model provide a foundation for subsequent research aimed at designing an algorithm that delivers an optimal or ε-optimal solution to the original problem, with some algorithmic details discussed herein. The model also paves the way for the development of a swift, cost-effective working set-like swapping algorithm, amplifying the applicability of the results obtained.