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

Jiang, Yunlian; Tian, Kai; Shen, Xipeng; Zhang, Jinghe; Chen, Jie; Tripathi, Rahul

doi:10.1109/tpds.2010.193

Cited by 18 publications

(22 citation statements)

References 20 publications

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“…As mentioned earlier, there have been some studies in optimal co-scheduling for minimum cost [10,11,24]. We have mentioned the connections and differences between that co-scheduling problem and our makespan minimization problem throughout this paper.…”

Section: Comparison With Cost Minimizationmentioning

confidence: 92%

“…Overall, the previous work on cost minimization [10,11,24] has given some insights to this work. But because of the different goals of the two problems, this systematic exploration is imperative for achieving a good understanding of the makespan minimization problem.…”

Section: Comparison With Cost Minimizationmentioning

confidence: 99%

“…. With Job Migrations Similar to the previous work [11], we use a search tree to model the co-scheduling problem when job migrations are allowed, as illustrated by Figure 3. It differs from Figure 2 in that each non-root node represents a sub-schedule (i.e., a set of assignments that cover all the unfinished jobs and have no overlap with each other) rather than a group of co-running jobs.…”

Section: Figmentioning

confidence: 99%

“…Despite that the two problems are both proved to be NPcomplete in a general setting, their proofs are substantially different. The previous work [10,11] analyzes the computation complexity of cost minimization by formulating the problem as an Multidimensional Assignment problem (MAP). But for makespan minimization, the MAP formulation cannot be applied because of the mismatch of the objectives.…”

Section: Comparison With Cost Minimizationmentioning

confidence: 99%

“…-Algorithms on Dual-Core Systems without Migrations. For algorithm design, the classic Blossom [6] algorithm can be directly used for finding the optimal schedule for dual-core cases for cost minimization [10,11]. But it cannot be applied to makespan minimization because the algorithm aims to minimizing the total weights of a perfect matching on a graph, rather than the largest weight as what makespan minimization requires.…”

Section: Comparison With Cost Minimizationmentioning

confidence: 99%

See 4 more Smart Citations

Optimal Co-Scheduling to Minimize Makespan on Chip Multiprocessors

Tian

Jiang

Shen

et al. 2013

Job Scheduling Strategies for Parallel Processing

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Abstract. On-chip resource sharing among sibling cores causes resource contention on Chip Multiprocessors (CMP), considerably degrading program performance and system fairness. Job co-scheduling attempts to alleviate the problem by assigning jobs to cores intelligently. Despite many heuristics-based empirical explorations, studies on optimal co-scheduling and its inherent complexity start only recently, and all have concentrated on the minimization of total performance degradations. There is another important criterion for scheduling, makespan, which determines the finish time of a job set. Its importance for job co-scheduling on CMP is increasingly recognized, especially with the rise of CMP-based compute cloud, data centers, and server farms. However, optimal coscheduling for makespan minimization still remains unexplored. This work compares makespan minimization problem with previously studied cost minimization (or degradation minimization) problem, revealing these connections as well as significant differences. It uncovers the computational complexity of the makespan minimization problem, and proposes a series of algorithms to either compute or approximate the optimal schedules. It proves that the problem is NP-complete in a general setting, but for a special case (dual-core without job migrations), the problem is solvable in O(n 2.5 · log n) time (n is the number of jobs). In addition, this paper presents a series of algorithms to compute or approximate the optimal schedules in the general setting. Experiments on both real and synthetic problems verify the optimality of the optimal co-scheduling algorithms, and demonstrate the reasonable accuracy and scalability of the approximation algorithms. The findings may advance the current understanding of optimal co-scheduling, facilitate the evaluation of real co-scheduling systems, and provide insights for the development of practical co-scheduling algorithms.

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Section: Comparison With Cost Minimizationmentioning

confidence: 92%

Section: Comparison With Cost Minimizationmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Comparison With Cost Minimizationmentioning

confidence: 99%