For hard-real time systems, cache memory increases execution time variability, increasing the complexity of timing analysis. As such, cache memory is often treated exclusively as a detractor to schedulability. Cache-aware co-located scheduling aims at improving schedulability by carefully scheduling threads to share cached values. Cache sharing between threads potentially reduces task execution times and increases schedulability with fewer resources. Antithetically, co-located scheduling may reduce parallelism, decreasing efficiency. Thus, identifying the optimal set of threads to co-locate that minimizes the resources required while ensuring timing constraints is a complex challenge. This work establishes optimal co-location as NP-Hard in the strong sense. It offers an approximation method for the co-located scheduling of Fork-Join tasks named 3-parm-hd . The approximation has a 3-factor guarantee and a resource augmentation bound of 3. The simulated evaluation shows 3-parm-hd increases schedulability compared to an optimal intractable algorithm (without co-location) scheduling 28% more tasks with 30% fewer cores. Simulated results show 3-parm-hd outperforms a 2-factor approximation for traditional makespan, scheduling 45 % more tasks with 41% fewer cores. An experimental RISC-V evaluation running on a QEMU platform confirms the benefits of 3-parm-hd , scheduling and executing tasks deemed unschedulable by a 2-factor makespan approximation without co-location.

For hard-real time systems, cache memory increases execution time variability, increasing the complexity of timing analysis. As such, cache memory is often treated exclusively as a detractor to schedulability. Cache-aware co-located scheduling aims to improve schedulability by carefully scheduling threads to share cached values. Cache sharing between threads potentially reduces task execution times and increases schedulability with fewer resources. Antithetically, co-located scheduling may reduce parallelism, decreasing efficiency. Thus, identifying the optimal set of threads to co-locate that minimizes the resources required while ensuring timing constraints is a complex challenge. This work establishes optimal co-location as NP-Hard in the strong sense. It offers an approximation method for the co-located scheduling of Fork-Join tasks named 3-PARM-HD. The approximation has a 3-factor guarantee and a resource augmentation bound of 3. The simulated evaluation shows 3-PARM-HD increases schedulability compared to an optimal intractable algorithm (without co-location) scheduling 28% more tasks with 30% fewer cores. Simulated results show 3-PARM-HD outperforms a 2-factor approximation for traditional makespan, scheduling 39% more tasks with 44% fewer cores. An experimental RISC-V evaluation running on a QEMU platform confirms the benefits of 3-PARM-HD, scheduling and executing tasks deemed unschedulable by a 2-factor makespan approximation without co-location.