Document Open Access Logo

Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model

Authors Anamitra Roy Choudhury, Syamantak Das, Amit Kumar

Thumbnail PDF


  • Filesize: 492 kB
  • 13 pages

Document Identifiers

Author Details

Anamitra Roy Choudhury
Syamantak Das
Amit Kumar

Cite AsGet BibTex

Anamitra Roy Choudhury, Syamantak Das, and Amit Kumar. Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 25-37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We consider the online scheduling problem to minimize the weighted ell_p-norm of flow-time of jobs. We study this problem under the rejection model introduced by Choudhury et al. (SODA 2015) - here the online algorithm is allowed to not serve an eps-fraction of the requests. We consider the restricted assignments setting where each job can go to a specified subset of machines. Our main result is an immediate dispatch non-migratory 1/eps^{O(1)}-competitive algorithm for this problem when one is allowed to reject at most eps-fraction of the total weight of jobs arriving. This is in contrast with the speed augmentation model under which no online algorithm for this problem can achieve a competitive ratio independent of p.
  • online scheduling
  • flow-time
  • competitive analysis


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Christoph Ambühl and Monaldo Mastrolilli. On-line scheduling to minimize max flow time: an optimal preemptive algorithm. Oper. Res. Lett., 33(6):597-602, 2005. Google Scholar
  2. S. Anand. Algorithms for flow time scheduling. PhD thesis, Indian Institute of Technology, Delhi, December 2013. Google Scholar
  3. S. Anand, Karl Bringmann, Tobias Friedrich, Naveen Garg, and Amit Kumar. Minimizing maximum (weighted) flow-time on related and unrelated machines. In ICALP (1), pages 13-24, 2013. Google Scholar
  4. S. Anand, Naveen Garg, and Amit Kumar. Resource augmentation for weighted flow-time explained by dual fitting. In SODA, pages 1228-1241, 2012. Google Scholar
  5. Nir Avrahami and Yossi Azar. Minimizing total flow time and total completion time with immediate dispatching. In SPAA, pages 11-18, 2003. Google Scholar
  6. Yossi Azar, Joseph (Seffi) Naor, and Raphael Rom. The competitiveness of on-line assignments. In Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms, pages 203-210, 1992. Google Scholar
  7. Nikhil Bansal, Avrim Blum, Shuchi Chawla, and Kedar Dhamdhere. Scheduling for flow-time with admission control. In Proc. ESA, 2003, 2003. Google Scholar
  8. Nikhil Bansal and Kirk Pruhs. Server scheduling in the l_p norm: a rising tide lifts all boat. In STOC, pages 242-250, 2003. Google Scholar
  9. Yair Bartal, Stefano Leonardi, Alberto Marchetti-Spaccamela, Jiri Sgall, and Leen Stougie. Multiprocessor scheduling with rejection. SIAM J. Discrete Math., 13(1):64-78, 2000. Google Scholar
  10. Jivitej S. Chadha, Naveen Garg, Amit Kumar, and V. N. Muralidhara. A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation. In STOC, pages 679-684, 2009. Google Scholar
  11. Ho-Leung Chan, Sze-Hang Chan, Tak Wah Lam, Lap-Kei Lee, and Jianqiao Zhu. Non-clairvoyant weighted flow time scheduling with rejection penalty. In SPAA, pages 246-254, 2012. Google Scholar
  12. Chandra Chekuri, Ashish Goel, Sanjeev Khanna, and Amit Kumar. Multi-processor scheduling to minimize flow time with epsilon resource augmentation. In STOC, pages 363-372, 2004. Google Scholar
  13. Anamitra Roy Choudhury, Syamantak Das, Naveen Garg, and Amit Kumar. Rejecting jobs to minimize load and maximum flow-time. In SODA, pages 1114-1133, 2015. Google Scholar
  14. Leah Epstein and Hanan Zebedat-Haider. Preemptive online scheduling with rejection of unit jobs on two uniformly related machines. J. Scheduling, 17(1):87-93, 2014. Google Scholar
  15. Naveen Garg and Amit Kumar. Better algorithms for minimizing average flow-time on related machines. In ICALP (1), pages 181-190, 2006. Google Scholar
  16. Naveen Garg and Amit Kumar. Minimizing average flow-time : Upper and lower bounds. In FOCS, pages 603-613, 2007. Google Scholar
  17. Daniel Golovin, Anupam Gupta, Amit Kumar, and Kanat Tangwongsan. All-norms and all-𝓁_p-norms approximation algorithms. In FSTTCS, pages 199-210, 2008. Google Scholar
  18. Sungjin Im and Benjamin Moseley. Online scalable algorithm for minimizing ;k-norms of weighted flow time on unrelated machines. In SODA, pages 95-108, 2011. Google Scholar
  19. Bala Kalyanasundaram and Kirk Pruhs. Speed is as powerful as clairvoyance. In FOCS, pages 214-221, 1995. Google Scholar
  20. Stefano Leonardi and Danny Raz. Approximating total flow time on parallel machines. J. Comput. Syst. Sci., 73(6):875-891, 2007. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail