Abstract
Multiprocessor scheduling, also called scheduling on parallel identical machines to minimize the makespan, is a classic optimization problem that has received numerous studies. Scheduling with testing is an online variant where the processing time of a job is revealed by an extra test operation, or otherwise the job has to be executed for a given upper bound on the processing time. Albers and Eckl recently studied the multiprocessor scheduling with testing; among others, for the non-preemptive setting they presented an approximation algorithm with competitive ratio approaching 3.1016 when the number of machines tends to infinity and an improved approximation algorithm with competitive ratio approaching 3 when all test operations take a time unit. We propose to first sort the jobs into the non-increasing order of the minimum value between the upper bound and the testing time, then partition the jobs into three groups and process them group by group according to the sorted job order. We show that our algorithm achieves improved competitive ratios, which approach 2.9513 when the number of machines tends to infinity in the general case; when all test operations take a time unit, our algorithm achieves even better competitive ratios approaching 2.8081.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albers, S., Eckl, A.: Explorable uncertainty in scheduling with non-uniform testing times. In: Kaklamanis, C., Levin, A. (eds.) WAOA 2020. LNCS, vol. 12806, pp. 127–142. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-80879-2_9
Albers, S., Eckl, A.: Scheduling with testing on multiple identical parallel machines. In: Lubiw, A., Salavatipour, M. (eds.) WADS 2021. LNCS, vol. 12808, pp. 29–42. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-83508-8_3
Cai, S.Y.: Semi online scheduling on three identical machines. J. Wenzhou Teach. Coll. 23, 1–3. (2002). (In Chinese)
Chen, B., Vliet, A., Woeginger, G.: New lower and upper bounds for on-line scheduling. Oper. Res. Lett. 16, 221–230 (1994)
Dürr, C., Erlebach, T., Megow, N., Meißner, J.: Scheduling with explorable uncertainty. In: ITCS 2018, pp. 30:1–14. LIPIcs 94 (2018), https://doi.org/10.4230/LIPIcs.ITCS.2018.30
Faigle, U., Kern, W., Turan, G.: On the performance of on-line algorithms for partition problems. Acta Cybern. 9, 107–119 (1989)
Fleischer, R., Wahl, M.: On-line scheduling revisited. J. Sched. 3, 343–353 (2000)
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Labs Tech. J. 45, 1563–1581 (1966)
He, Y., Zhang, G.: Semi online scheduling on two identical machines. Computing 62, 179–187 (1999)
Lee, K., Lim, K.: Semi-online scheduling problems on a small number of machines. J. Sched. 16, 461–477 (2003)
Rudin III, J.F.: Improved bounds for the on-line scheduling problem. Ph.D. thesis (2001)
Rudin, J.F., III., Chandrasekaran, R.: Improved bound for the online scheduling problem. SIAM J. Comput. 32, 717–735 (2003)
Tan, Z., Li, R.Q.: Pseudo lower bounds for online parallel machine scheduling. Oper. Res. Lett. 43, 489–494 (2015)
Wu, Y., Huang, Y., Yang, Q.F.: Semi-online multiprocessor scheduling with the longest given processing time. J. Zhejiang Univ. Sci. Edn. 35, 23–26 (2008). (in Chinese)
Acknowledgments
This research is supported by the NSERC Canada.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Gong, M., Lin, G. (2022). Improved Approximation Algorithms for Multiprocessor Scheduling with Testing. In: Chen, J., Li, M., Zhang, G. (eds) Frontiers of Algorithmics. IJTCS-FAW 2021. Lecture Notes in Computer Science(), vol 12874. Springer, Cham. https://doi.org/10.1007/978-3-030-97099-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-97099-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-97098-7
Online ISBN: 978-3-030-97099-4
eBook Packages: Computer ScienceComputer Science (R0)