Document Open Access Logo

Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs

Authors Danny Hermelin, Judith-Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, Gerhard Woeginger

PDF
Thumbnail PDF

File

LIPIcs.IPEC.2015.55.pdf
  • Filesize: 446 kB
  • 11 pages

Document Identifiers

Author Details

Danny Hermelin
Judith-Madeleine Kubitza
Dvir Shabtay
Nimrod Talmon
Gerhard Woeginger

Cite AsGet BibTex

Danny Hermelin, Judith-Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, and Gerhard Woeginger. Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 55-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.IPEC.2015.55

Abstract

We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters. We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.
Keywords
  • Parameterized Complexity
  • Multiagent Scheduling

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Alessandro Agnetis, Jean-Charles Billaut, Stanisław Gawiejnowicz, Dario Pacciarelli, and Ameur Soukhal. Multiagent Scheduling: Models and Algorithms. Springer, 2014. Google Scholar
  2. Allesandro Agnetis, Pitu B. Mirchandani, Dario Pacciarelli, and Andrea Pacifici. Scheduling problems with two competing agents. Operations Research, 52(2):229-242, 2004. Google Scholar
  3. Kenneth R. Baker and J. Cole Smith. A multiple-criterion model for machine scheduling. Journal of Scheduling, 6(1):7-16, 2003. Google Scholar
  4. René Bevernvan Bevern, Matthias Mnich, Rolf Niedermeier, and Mathias Weller. Interval scheduling and colorful independent sets. In Proceedings of the 23th International Symposium on Algorithms and Computation (ISAAC'12), volume 7676 of LNCS, pages 247-256. Springer, 2012. Google Scholar
  5. René Bevernvan Bevern, Rolf Niedermeier, and Ondrej Suchý. A parameterized complexity view on non-preemptively scheduling interval-constrained jobs: few machines, small looseness, and small slack. arXiv preprint arXiv:1005.4159, 2015. Google Scholar
  6. Hans L. Bodlaender and Michael R. Fellows. W[2]-hardness of precedence constrained k-processor scheduling. Operations Research Letters, 18(2):93-97, 1995. Google Scholar
  7. Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Piotr Skowron, and Nimrod Talmon. Elections with few candidates: Prices, weights, and covering problems. In Proceedings of the 4th International Conference on Algorithmic Decision Theory (ADT'15), pages 414-431. Springer, 2015. Google Scholar
  8. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Springer, 2013. Google Scholar
  9. Michael R. Fellows and Catherine McCartin. On the parametric complexity of schedules to minimize tardy tasks. Theoretical computer science, 298(2):317-324, 2003. Google Scholar
  10. Jörg Flum and Martin Grohe. Parameterized Complexity Theory. Springer, 2006. Google Scholar
  11. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979. Google Scholar
  12. Magnús M. Halldórsson and Ragnar K. Karlsson. Strip graphs: Recognition and scheduling. In Proceedings of the 32th International Workshop on Graph-Theoretic Concepts in Computer Science (WG'06), volume 4271 of LNCS, pages 137-146. Springer, 2006. Google Scholar
  13. Mikhail Y. Kovalyov, Ammar Oulamara, and Ameur Soukhal. Two-agent scheduling on an unbounded serial batching machine. In Proceedings of the Second International Symposium on Combinatorial Optimization (ISCO'12), volume 3787 of LNCS, pages 427-438. Springer, 2012. Google Scholar
  14. Kangbok Lee, Byung-Cheon Choi, Joseph Y.-T. Leung, and Michael L. Pinedo. Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Information Processing Letters, 109(16):913-917, 2009. Google Scholar
  15. Hendrik W. Lenstra. Integer programming with a fixed number of variables. \bibremarkNo string.Mathematics of Operations Research\bibremarkNo publisher., 8(4):538-548, 1983. Google Scholar
  16. Joseph Y.-T. Leung, Michael Pinedo, and Guohua Wan. Competitive two-agent scheduling and its applications. Operations Research, 58(2):458-469, 2010. Google Scholar
  17. Matthias Mnich and Andreas Wiese. Scheduling and fixed-parameter tractability. In Proceedings of the 17th International Conference on Integer Programming and Combinatorial Optimizationon (IPCO'14), volume 8494 of LNCS, pages 381-392. Springer, 2014. Google Scholar
  18. Baruch Mor and Gur Mosheiov. Single machine batch scheduling with two competing agents to minimize total flowtime. European Journal of Operational Research, 215(3):524-531, 2011. Google Scholar
  19. Rolf Niedermeier. Invitation to fixed-parameter algorithms. Habilitation thesis, Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, September 2002. Google Scholar
  20. Daniel Oron, Dvir Shabtay, and George Steiner. Single machine scheduling with two competing agents and equal job processing times. European Journal of Operational Research, 2015. Google Scholar
  21. Paz Perez-Gonzalez and Jose M. Framinan. A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems. European Journal of Operational Research, 235(1):1-16, 2014. Google Scholar
  22. Michael L. Pinedo. Scheduling: theory, algorithms, and systems. Springer Science & Business Media, 2012. Google Scholar
  23. Jinjiang Yuan, Weiping Shang, and Qi Feng. A note on the scheduling with two families of jobs. Journal of Scheduling, 8(6):537-542, 2005. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact