Document Open Access Logo

Scheduling with Locality by Routing

Authors Alison Hsiang-Hsuan Liu , Fu-Hong Liu

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2024.69.pdf
  • Filesize: 4.78 MB
  • 15 pages

Document Identifiers

Author Details

Alison Hsiang-Hsuan Liu
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Fu-Hong Liu
  • Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan

Acknowledgements

The authors would like to thank Sheng-Yin Chen and Chung-Shou Liao for their discussions in the early stages.

Cite As Get BibTex

Alison Hsiang-Hsuan Liu and Fu-Hong Liu. Scheduling with Locality by Routing. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 69:1-69:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.69

Abstract

This work examines a strongly NP-hard routing problem on trees, in which multiple servers need to serve a given set of requests (on vertices), where the routes of the servers start from a common source and end at their respective terminals. Each server can travel free of cost on its source-to-terminal path but has to pay for travel on other edges. The objective is to minimize the maximum cost over all servers. As the servers may pay different costs for traveling through a common edge, balancing the loads of the servers can be difficult. We propose a polynomial-time 4-approximation algorithm that applies the parametric pruning framework but consists of two phases. The first phase of the algorithm partitions the requests into packets, and the second phase of the algorithm assigns the packets to the servers. Unlike the standard parametric pruning techniques, the challenge of our algorithm design and analysis is to harmoniously relate the quality of the partition in the first phase, the balances of the servers' loads in the second phase, and the hypothetical optimal values of the framework. For the problem in general graphs, we show that there is no algorithm better than 2-approximate unless P = NP. The problem is a generalization of unrelated machine scheduling and other classic scheduling problems. It also models scheduling problems where the job processing times depend on the machine serving the job and the other jobs served by that machine. This modeling provides a framework that physicalizes scheduling problems through the graph’s point of view.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Makespan minimization
  • Approximation algorithms
  • Routing problems
  • Parametric pruning framework

Metrics

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

References

  1. Ali Allahverdi. The third comprehensive survey on scheduling problems with setup times/costs. Eur. J. Oper. Res., 246(2):345-378, 2015. URL: https://doi.org/10.1016/j.ejor.2015.04.004.
  2. Dor Arad, Yael Mordechai, and Hadas Shachnai. Tighter bounds for makespan minimization on unrelated machines. CoRR, abs/1405.2530, 2014. URL: https://arxiv.org/abs/1405.2530.
  3. Esther M. Arkin, Refael Hassin, and Asaf Levin. Approximations for minimum and min-max vehicle routing problems. J. Algorithms, 59(1):1-18, 2006. URL: https://doi.org/10.1016/j.jalgor.2005.01.007.
  4. Tetsuo Asano, Naoki Katoh, Hisao Tamaki, and Takeshi Tokuyama. Covering points in the plane by k-tours: Towards a polynomial time approximation scheme for general k. In Frank Thomson Leighton and Peter W. Shor, editors, Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, 1997, pages 275-283. ACM, 1997. URL: https://doi.org/10.1145/258533.258602.
  5. Tolga Bektas and Adam N. Letchford. Using 𝓁^p-norms for fairness in combinatorial optimisation. Comput. Oper. Res., 120:104975, 2020. URL: https://doi.org/10.1016/j.cor.2020.104975.
  6. Binay K. Bhattacharya and Yuzhuang Hu. k-delivery traveling salesman problem on tree networks. In Deepak D'Souza, Telikepalli Kavitha, and Jaikumar Radhakrishnan, editors, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2012, December 15-17, 2012, Hyderabad, India, volume 18 of LIPIcs, pages 325-336. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2012.325.
  7. Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu. Traveling repairperson, unrelated machines, and other stories about average completion times. In Nikhil Bansal, Emanuela Merelli, and James Worrell, editors, 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), volume 198 of LIPIcs, pages 28:1-28:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.28.
  8. Adrian Bock, Elyot Grant, Jochen Könemann, and Laura Sanità. The school bus problem on trees. Algorithmica, 67(1):49-64, 2013. Google Scholar
  9. Kris Braekers, Katrien Ramaekers, and Inneke Van Nieuwenhuyse. The vehicle routing problem: State of the art classification and review. Comput. Ind. Eng., 99:300-313, 2016. Google Scholar
  10. John L. Bruno and Peter J. Downey. Complexity of task sequencing with deadlines, set-up times and changeover costs. SIAM J. Comput., 7(4):393-404, 1978. URL: https://doi.org/10.1137/0207031.
  11. Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, and Maria Kyropoulou. The efficiency of fair division. Theory Comput. Syst., 50(4):589-610, 2012. Google Scholar
  12. L. Chen, K. Jansen, and G. Zhang. On the optimality of approximation schemes for the classical scheduling problem. In 25th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 657-668, 2014. Google Scholar
  13. Shichuan Deng, Jian Li, and Yuval Rabani. Generalized unrelated machine scheduling problem. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 2898-2916. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch110.
  14. Alexander Fuerst and Prateek Sharma. Locality-aware load-balancing for serverless clusters. In Jon B. Weissman, Abhishek Chandra, Ada Gavrilovska, and Devesh Tiwari, editors, HPDC '22: The 31st International Symposium on High-Performance Parallel and Distributed Computing, Minneapolis, MN, USA, 27 June 2022 - 1 July 2022, pages 227-239. ACM, 2022. URL: https://doi.org/10.1145/3502181.3531459.
  15. Martin Gairing, Burkhard Monien, and Andreas Woclaw. A faster combinatorial approximation algorithm for scheduling unrelated parallel machines. Theor. Comput. Sci., 380(1-2):87-99, 2007. URL: https://doi.org/10.1016/j.tcs.2007.02.056.
  16. Maxime Gonthier, Loris Marchal, and Samuel Thibault. Locality-aware scheduling of independent tasks for runtime systems. In Ricardo Chaves, Dora B. Heras, Aleksandar Ilic, Didem Unat, Rosa M. Badia, Andrea Bracciali, Patrick Diehl, Anshu Dubey, Oh Sangyoon, Stephen L. Scott, and Laura Ricci, editors, Euro-Par 2021: Parallel Processing Workshops - Euro-Par 2021 International Workshops, Lisbon, Portugal, August 30-31, 2021, Revised Selected Papers, volume 13098 of Lecture Notes in Computer Science, pages 5-16. Springer, 2021. URL: https://doi.org/10.1007/978-3-031-06156-1_1.
  17. Sungjin Im and Shi Li. Improved approximations for unrelated machine scheduling. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 2917-2946. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch111.
  18. Klaus Jansen, Marten Maack, and Alexander Mäcker. Scheduling on (un-)related machines with setup times. In 2019 IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019, Rio de Janeiro, Brazil, May 20-24, 2019, pages 145-154. IEEE, 2019. URL: https://doi.org/10.1109/IPDPS.2019.00025.
  19. Hessam Kooti and Eli Bozorgzadeh. Reconfiguration-aware task graph scheduling. In Eli Bozorgzadeh, João M. P. Cardoso, Rui Abreu, and Seda Ogrenci Memik, editors, 13th IEEE International Conference on Embedded and Ubiquitous Computing, EUC 2013, Porto, Portugal, October 21-23, 2015, pages 163-167. IEEE Computer Society, 2015. URL: https://doi.org/10.1109/EUC.2015.33.
  20. Jan Karel Lenstra, David B. Shmoys, and Éva Tardos. Approximation algorithms for scheduling unrelated parallel machines. In 28th Annual Symposium on Foundations of Computer Science, Los Angeles, California, USA, 27-29 October 1987, pages 217-224. IEEE Computer Society, 1987. URL: https://doi.org/10.1109/SFCS.1987.8.
  21. Jan Karel Lenstra, David B. Shmoys, and Éva Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Program., 46:259-271, 1990. URL: https://doi.org/10.1007/BF01585745.
  22. Alexander Mäcker, Manuel Malatyali, Friedhelm Meyer auf der Heide, and Sören Riechers. Non-preemptive scheduling on machines with setup times. In Frank Dehne, Jörg-Rüdiger Sack, and Ulrike Stege, editors, Algorithms and Data Structures - 14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015. Proceedings, volume 9214 of Lecture Notes in Computer Science, pages 542-553. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21840-3_45.
  23. Jurij Mihelic and Borut Robic. Solving the k-center problem efficiently with a dominating set algorithm. J. Comput. Inf. Technol., 13(3):225-234, 2005. URL: https://doi.org/10.2498/cit.2005.03.05.
  24. Mary Monroe and David M. Mount. A PTAS for the min-max euclidean multiple TSP. CoRR, abs/2112.04325, 2021. URL: https://arxiv.org/abs/2112.04325.
  25. Javier Resano, Daniel Mozos, Diederik Verkest, Serge Vernalde, and Francky Catthoor. Run-time minimization of reconfiguration overhead in dynamically reconfigurable systems. In Peter Y. K. Cheung, George A. Constantinides, and José T. de Sousa, editors, Field Programmable Logic and Application, 13th International Conference, FPL 2003, Lisbon, Portugal, September 1-3, 2003, Proceedings, volume 2778 of Lecture Notes in Computer Science, pages 585-594. Springer, 2003. URL: https://doi.org/10.1007/978-3-540-45234-8_57.
  26. Ola Svensson. Santa claus schedules jobs on unrelated machines. SIAM J. Comput., 41(5):1318-1341, 2012. URL: https://doi.org/10.1137/110851201.
  27. Zhou Xu and Brian Rodrigues. A 3/2-approximation algorithm for multiple depot multiple traveling salesman problem. In Haim Kaplan, editor, Algorithm Theory - SWAT 2010, 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings, volume 6139 of Lecture Notes in Computer Science, pages 127-138. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-13731-0_13.
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 About DROPS Imprint Privacy Contact