Dynamic scheduling on parallel machines
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Complexity of scheduling multiprocessor tasks with prespecified processor allocations
Discrete Applied Mathematics
Scheduling parallel tasks to minimize average response time
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Scheduling Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
On-line scheduling on a single machine: maximizing the number of early jobs
Operations Research Letters
Maximizing the throughput of parallel jobs on hypercubes
Information Processing Letters
Scheduling multiprocessor UET tasks of two sizes
Theoretical Computer Science
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We consider the problem of scheduling n independent multiprocessor tasks with due dates and unit processing times, where the objective is to compute a schedule maximizing the throughput. We derive the complexity results and present several approximation algorithms. For the parallel variant of the problem, we introduce the first-fit increasing algorithm and the latest-fit increasing algorithm, and prove that their worst-case ratios are 2 and 2 - 1/m, respectively (m ≥ 2 is the number of processors). Then we propose a revised algorithm with a worst-case ratio bounded by 3/2- 1/(2m) (m is odd) and 3/2-1/(2m-2) (m is even). For the dedicated variant, we present a simple greedy algorithm. We show that its worst-case ratio is bounded by √m + 1. We straighten this result by showing that the problem cannot be approximated within a factor of m1/2-ε for any ε 0, unless NP = ZPP.