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

Abstract

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.