在嵌入式系統環境中，許多的資源限制導致一般的列表排程演算法無法找到 符合的排程。在有記憶體限制及高度平行度的情況下，對於排程演算法其中 一個很大的挑戰是死結。在這篇文章中，我們將首要的目標定為:在給定記 憶體的限制下，找到符合的排程。我們提出了一個基於預約的演算法且可以 整合進一般的列表排程演算法中使該演算法將記憶體限制納入考量。我們提 出的方法可以有效的避免死結的產生並且大幅度的減少所需的記憶體用量。 實驗結果顯示不論是在隨機產生的圖或是現實中的應用，我們的方法皆能得 到品質更好的排程結果-平均縮短 10% 的執行時間以及減少 30% 的記憶體使 用量。

Many embedded systems have hard resource constraints that make schedules found by list scheduling heuristics infeasible. One of the main challenges yielded by memory constraints and the high degree of parallelism is deadlock. In this paper, our primary goal is to find a feasible solution given the memory constraints. We propose a reservation-based solution, an extension for list scheduling algorithms, that can be integrated into those algorithms and make them aware of memory con- straints. We show our technique prevents deadlock and significantly reduces the required memory size. The experimental results on randomly generated graphs and real world applications show that our proposed solution can obtain relatively high- quality solutions with up to 10% makespan improvement and 30% memory reduc- tion on average.

1 Introduction 1
2 Challenges: Scheduling with memory constraints 4
2.1 Memoryconstraints.......................... 4
2.2 The problem caused by memory constraints: Deadlock . . . . . . . 5 2.3 MotivationExample ......................... 5
3 Problem Modeling 8 3.1 ProgramPerspective ......................... 9
3.2 MemoryModel ............................ 9
3.3 ListSchedulingDefinition ...................... 10
4 Related Work 12
4.1 SchedulingwithSharedMemoryConstraints . . . . . . . . . . . . 12 4.2 Analysis................................ 13
5 Proposed Solution 14
5.1 Issueswithexistingsolutions..................... 14
5.2 Goal.................................. 15
5.3 Reservation-basedalgorithm ..................... 16
5.4 Timecomplexity ........................... 20
6 Experimental results 21
6.1 Randomworkflowsgenerator. .................... 21
6.2 Impactofdepthk ........................... 22
6.3 Minimummemoryusage....................... 23
6.4 Evaluationonrealworldapplications ................ 24
6.5 Minimized makespan value under memory constraints . . . . . . . 26
6.6 Applicability ............................. 27
7 Conclusions 28
References 29

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