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The Complexity of Optimal Job Co-Scheduling on Chip Multiprocessors and Heuristics-Based Solutions

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6 Author(s)
Yunlian Jiang ; Dept. of Comput. Sci., Coll. of William & Mary, Williamsburg, VA, USA ; Kai Tian ; Xipeng Shen ; Jinghe Zhang
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In Chip Multiprocessors (CMPs) architecture, it is common that multiple cores share some on-chip cache. The sharing may cause cache thrashing and contention among co-running jobs. Job co-scheduling is an approach to tackling the problem by assigning jobs to cores appropriately so that the contention and consequent performance degradations are minimized. Job co-scheduling includes two tasks: the estimation of co-run performance, and the determination of suitable co-schedules. Most existing studies in job co-scheduling have concentrated on the first task but relies on simple techniques (e.g., trying different schedules) for the second. This paper presents a systematic exploration to the second task. The paper uncovers the computational complexity of the determination of optimal job co-schedules, proving its NP-completeness. It introduces a set of algorithms, based on graph theory and Integer/Linear Programming, for computing optimal co-schedules or their lower bounds in scenarios with or without job migrations. For complex cases, it empirically demonstrates the feasibility for approximating the optimal effectively by proposing several heuristics-based algorithms. These discoveries may facilitate the assessment of job co-schedulers by providing necessary baselines, as well as shed insights to the development of co-scheduling algorithms in practical systems.

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:22 ,  Issue: 7 )