Minimizing mean flow time with release time constraint
Theoretical Computer Science
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Mathematical Programming: Series A and B
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
On-line scheduling of a single machine to minimize total weighted completion time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal On-Line Algorithms for Single-Machine Scheduling
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Scheduling Jobs that Arrive Over Time (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On-line scheduling of parallel machines to minimize total completion times
Computers and Operations Research
LP-based online scheduling: from single to parallel machines
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
A class of on-line scheduling algorithms to minimize total completion time
Operations Research Letters
On-line scheduling to minimize average completion time revisited
Operations Research Letters
Efficient algorithms for average completion time scheduling
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Completion time scheduling and the WSRPT algorithm
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
An improved analysis of SRPT scheduling algorithm on the basis of functional optimization
Information Processing Letters
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We consider the classical problem of scheduling preemptible jobs, that arrive over time, on identical parallel machines. The goal is to minimize the total completion time of the jobs. In standard scheduling notation of Graham et al. [5], this problem is denoted P|rj, pmtn|Σj/cj. A popular algorithm called SRPT, which always schedules the unfinished jobs with shortest remaining processing time, is known to be 2-competitive, see Phillips et al. [13, 14]. This is also the best known competitive ratio for any online algorithm. However, it is conjectured that the competitive ratio of SRPT is significantly less than 2. Even breaking the barrier of 2 is considered a significant step towards the final answer of this classical online problem. We improve on this open problem by showing that SRPT is 1.86-competitive. This result is obtained using the following method, which might be of general interest: We define two dependent random variables that sum up to the difference between the cost of an SRPT schedule and the cost of an optimal schedule. Then we bound the sum of the expected values of these random variables with respect to the cost of the optimal schedule, yielding the claimed competitiveness. Furthermore, we show a lower bound of 21/19 for SRPT, improving on the previously best known 12/11 due to Lu et al. [11].