Document Open Access Logo

Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

Authors George Karakostas, Stavros G. Kolliopoulos

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2023.5.pdf
  • Filesize: 0.74 MB
  • 17 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • scheduling
  • maximum weighted throughput
  • unrelated machines
  • approximation algorithm
  • PTAS

Metrics

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

Abstract

We study the classic weighted maximum throughput problem on unrelated machines. We give a (1-1/e-ε)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ-approximation algorithm for the single-machine problem to obtain an approximation factor of (1-1/e)ρ -ε for the corresponding unrelated-machines problem, for any ε > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1-1/e) -ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine.

Cite As Get BibTex

George Karakostas and Stavros G. Kolliopoulos. Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.5

Author Details

George Karakostas
  • Department of Computing & Software, McMaster University, Hamilton, Canada
Stavros G. Kolliopoulos
  • Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece

Funding

  • Kolliopoulos, Stavros G.: Travel support was provided by the Faculty of Science of the National and Kapodistrian University of Athens.

References

  1. P. Baptiste. Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times. Journal of Scheduling, 2(6):245-252, 1999. Google Scholar
  2. A. Bar-Noy, R. Bar-Yehuda, A. Freund, J. Naor, and B. Schieber. A unified approach to approximating resource allocation and scheduling. J. ACM, 48(5):1069-1090, 2001. Google Scholar
  3. A. Bar-Noy, S. Guha, J. Naor, and B. Schieber. Approximating the throughput of multiple machines in real-time scheduling. SIAM J. Comput., 31(2):331-352, 2001. Google Scholar
  4. P. Berman and B. DasGupta. Improvements in throughout maximization for real-time scheduling. In 32nd Annual ACM Symposium on Theory of Computing (STOC), pages 680-687. ACM, 2000. Google Scholar
  5. M. Böhm, N. Megow, and J. Schlöter. Throughput scheduling with equal additive laxity. Oper. Res. Lett., 50(5):463-469, 2022. Google Scholar
  6. J. Chuzhoy, R. Ostrovsky, and Y. Rabani. Approximation algorithms for the job interval selection problem and related scheduling problems. Math. Oper. Res., 31(4):730-738, 2006. Google Scholar
  7. F. Eberle, N. Megow, and K. Schewior. Online throughput maximization on unrelated machines: Commitment is no burden. ACM Trans. Algorithms, 19(1):10:1-10:25, 2023. Google Scholar
  8. L. Fleischer, M. X. Goemans, V. S. Mirrokni, and M. Sviridenko. Tight approximation algorithms for maximum separable assignment problems. Math. Oper. Res., 36(3):416-431, 2011. Google Scholar
  9. R. Gandhi, S. Khuller, S. Parthasarathy, and A. Srinivasan. Dependent rounding and its applications to approximation algorithms. J. ACM, 53(3):324-360, 2006. Google Scholar
  10. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, 1979. Google Scholar
  11. D. Hyatt-Denesik, M. Rahgoshay, and M. R. Salavatipour. Approximations for throughput maximization. In 31st Int. Symp. on Algorithms and Computation, ISAAC 2020, volume 181 of LIPIcs, pages 11:1-11:17, 2020. Google Scholar
  12. S. Im, S. Li, and B. Moseley. Breaking the 1 - 1/e barrier for nonpreemptive throughput maximization. SIAM J. Discret. Math., 34(3):1649-1669, 2020. Google Scholar
  13. B. Kalyanasundaram and K. Pruhs. Eliminating migration in multi-processor scheduling. J. Algorithms, 38(1):2-24, 2001. Google Scholar
  14. R. M. Karp. Reducibility among combinatorial problems. In Complexity of Computer Computations, pages 85-103. Plenum Press, 1972. Google Scholar
  15. A. Khan, E. Sharma, and K. V. N. Sreenivas. Approximation algorithms for generalized multidimensional knapsack. CoRR, abs/2102.05854, 2021. URL: https://arxiv.org/abs/2102.05854.
  16. E. L. Lawler. Recent results in the theory of machine scheduling. In Mathematical Programming The State of the Art, XIth Int. Symp. on Math. Programming, pages 202-234. Springer, 1983. Google Scholar
  17. E. L. Lawler. A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs. Ann. Oper. Res., 26(1-4):125-133, 1990. Google Scholar
  18. E. L. Lawler, J. K. Lenstra, A. H. G. Rinooy Kan, and D. B. Shmoys. Sequencing and scheduling: Algorithms and complexity. In S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, editors, Handbooks in Operations Research and Management Science, Vol 4., Logistics of Production and Inventory, pages 445-522. North Holland, 1993. Google Scholar
  19. K. Pruhs and G. J. Woeginger. Approximation schemes for a class of subset selection problems. Theor. Comput. Sci., 382(2):151-156, 2007. Google Scholar
  20. A. Schrijver. Theory of linear and integer programming. John Wiley and Sons, 1986. Google Scholar
  21. A. Srinivasan. Distributions on level-sets with applications to approximation algorithms. In 42nd IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages 588-597, 2001. 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
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact