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
On Minimizing Average Weighted Completion Time of Multiprocessor Tasks with Release Dates
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Scheduling to Minimize the Average Completion Time of Dedicated Tasks
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
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
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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 驴 2 is the number of processors). Then we propose a revised algorithm with worst-case ratio bounded by 3/2 - 1/(2m - 2) (m is even) and 3/2 - 1/(2m) (m is odd). For the dedicated variant, we present a simple greedy algorithm. We show that its worst-case ratio is bounded by 驴m+1. We straighten this result by showing that the problem (even for a common due date D = 1) cannot be approximated within a factor of m1/2-驴 for any 驴 0, unless NP = ZPP.