SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Patience is a virtue: the effect of slack on competitiveness for admission control
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Online scheduling with hard deadlines
Journal of Algorithms
Extra processors versus future information in optimal deadline scheduling
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Online deadline scheduling with preemption penalties
Computers and Industrial Engineering
Online scheduling with hard deadlines on parallel machines
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Maximizing the throughput of multiple machines on-line
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
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We study the competitiveness of online deadline scheduling problems. It is assumed that jobs are non-preemptive and we want to maximize, in an online manner, the sum of the length of jobs completed before their deadlines. When there is a single machine, Goldwasser [4] showed that the optimal deterministic competitiveness of this problem is 2+1/k, where each job of length L can be delayed for at least k • L before it is started, while still meeting its deadline. We consider the case that k O((log 1/k ))-competitive randomized algorithm not only for a single machine but also for m machines where m = 1,2,•••, O(( log 1/k )).Of particular interest is our technique: we mainly consider deterministic algorithms for multiple machines in order to improve the randomized competitiveness for a single (or more) machine. Though this approach is not completely new, it is rather complicated in our case to design a deterministic algorithm for multiple machines. Specifically, we present an [m+1+ m • (1/k)(1/m)]-competitive deterministic algorithm, where m (≥ 2) machines are available to both online algorithms and the adversary.Finally we also study a related problem and present an improved algorithm.