Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Theory and Practice in Parallel Job Scheduling
IPPS '97 Proceedings of the Job Scheduling Strategies for Parallel Processing
Developments from a June 1996 seminar on Online algorithms: the state of the art
Online Scheduling to Minimize Average Stretch
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Scheduling malleable tasks with precedence constraints
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Preemptable Malleable Task Scheduling Problem
IEEE Transactions on Computers
Scheduling parallel jobs to minimize the makespan
Journal of Scheduling
Online malleable job scheduling for m≤3
Information Processing Letters
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In this paper, we study a parallel job scheduling model which takes into account both computation time and the overhead from communication between processors. Assuming that a job Jj has a processing requirement pj and is assigned to kj processors for parallel execution, then the execution time will be modeled by tj = pj / kj + (kj - 1) · c, where c is the constant overhead cost associated with each processor other than the master processor. In this model, (kj - 1) · c represents the cost for communication and coordination among the processors. This model attempts to accurately portray the actual execution time for jobs running in parallel on multiple processors. Using this model, we will study the online algorithm Earliest Completion Time (ECT) and show a lower bound for the competitive ratio of ECT for m ≥ 2 processors. For m ≤ 4, we show the matching upper bound to complete the competitive analysis for m = 2, 3, 4. For large m, we conjecture that the ratio approaches 30/13 ≈ 2.30769.