Scheduling MapReduce Jobs under Multi-Round Precedences

We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on identical and unrelated parallel processors. For identical processors, we present LP-based O(1)-approximation algorithms. For unrelated processors, the approximation ratio naturally depends on the maximum number of rounds of any job. Since the number of rounds per job in typical MapReduce algorithms is a small constant, our scheduling algorithms achieve a small approximation ratio in practice. For the single-round case, we substantially improve on previously best known approximation guarantees for both identical and unrelated processors. Moreover, we conduct an experimental analysis and compare the performance of our algorithms against a fast heuristic and a lower bound on the optimal solution, thus demonstrating their promising practical performance

Hardness of Approximating Flow and Job Shop Scheduling Problems

We consider several variants of the job shop problem that is a fundamental and classical problem in scheduling. The currently best approximation algorithms have worse than logarithmic performance guarantee, but the only previously known inapproximability result says that it is NP-hard to approximate job shops within a factor less than 5/4. Closing this big approximability gap is a well-known and long-standing open problem