Improved bicriteria existence theorems for scheduling
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Existence theorems, lower bounds and algorithms for scheduling to meet two objectives
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Existence Theorems for Scheduling to Meet Two Objectives
Existence Theorems for Scheduling to Meet Two Objectives
Operations Research Letters
Approximation algorithms for the bi-criteria weighted MAX-CUT problem
Discrete Applied Mathematics
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We study the problem of simultaneously minimizing the makespan and the average weighted completion time for the precedence multiprocessor constrained scheduling problem with unit execution times and unit communication delays, known as the UET--UCT problem (Munier and König, Operations Research, 45(1), 145--148 (1997)). We propose a simple (16/9, 16/9)-approximation algorithm for the problem with an unrestricted number of machines. We improve our algorithm by adapting a technique first introduced by Aslam et al. (Proceedings of ACM-SODA, pp. 846--847, 1999) and provide a (1.745, 1.745)-approximate solution. For the considered scheduling problem, we prove the existence of a (1.445, 1.445)-approximate solution, improving the generic existence result of Aslam et al. (Proceedings of ACM-SODA, pp. 846--847, 1999). Also notice that our results for the case of an unrestricted number of processors hold for the more general scheduling problem with small communication delays (SCT problem), and for two other classical optimality criteria: maximum lateness and weighted lateness. Finally, we propose an approximation algorithm for the UET--UCT problem with a restricted number of processors.