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Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, Seeun William Umboh

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Set Cover
  • Joint Replenishment
  • TCP-Acknowledgment
  • Subadditive Function Approximation
  • Multi-Level Aggregation

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Abstract

The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types.
We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.

Cite As Get BibTex

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.12

Author Details

Tomer Ezra
  • Harvard University, Cambridge, MA, USA
Stefano Leonardi
  • Sapienza University of Rome, Italy
Michał Pawłowski
  • MIMUW, University of Warsaw, Poland
  • IDEAS NCBR, Warsaw, Poland
Matteo Russo
  • Sapienza University of Rome, Italy
Seeun William Umboh
  • School of Computing and Information Systems, The University of Melbourne, Australia
  • ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA), Melbourne, Australia

Funding

  • Ezra, Tomer: Supported by the Harvard University Center of Mathematical Sciences and Applications.
  • Leonardi, Stefano: Supported by the ERC Advanced Grant 788893 AMDROMA and MIUR PRIN project ALGADIMAR.
  • Russo, Matteo: Supported by the ERC Advanced Grant 788893 AMDROMA and MIUR PRIN project ALGADIMAR.
  • Umboh, Seeun William: Part of this work was done when the author was visiting the Sapienza University of Rome, and at the School of Computer Science, University of Sydney.

Acknowledgements

We thank the anonymous reviewers for their valuable feedback.

References

  1. Itai Ashlagi, Yossi Azar, Moses Charikar, Ashish Chiplunkar, Ofir Geri, Haim Kaplan, Rahul Makhijani, Yuyi Wang, and Roger Wattenhofer. Min-cost bipartite perfect matching with delays. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2017, volume 81 of LIPIcs, pages 1:1-1:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.1.
  2. Yossi Azar, Ashish Chiplunkar, and Haim Kaplan. Polylogarithmic bounds on the competitiveness of min-cost perfect matching with delays. In Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, pages 1051-1061. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.67.
  3. Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou. Set cover with delay - Clairvoyance is not required. In Fabrizio Grandoni, Grzegorz Herman, and Peter Sanders, editors, 28th Annual European Symposium on Algorithms, ESA 2020, September 7-9, 2020, Pisa, Italy (Virtual Conference), volume 173 of LIPIcs, pages 8:1-8:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ESA.2020.8.
  4. Yossi Azar and Amit Jacob Fanani. Deterministic min-cost matching with delays. Theory Comput. Syst., 64(4):572-592, 2020. URL: https://doi.org/10.1007/s00224-019-09963-7.
  5. Yossi Azar, Arun Ganesh, Rong Ge, and Debmalya Panigrahi. Online service with delay. ACM Trans. Algorithms, 17(3):23:1-23:31, 2021. URL: https://doi.org/10.1145/3459925.
  6. Yossi Azar, Runtian Ren, and Danny Vainstein. The min-cost matching with concave delays problem. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, pages 301-320. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.20.
  7. Yossi Azar and Noam Touitou. General framework for metric optimization problems with delay or with deadlines. In David Zuckerman, editor, 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019, Baltimore, Maryland, USA, November 9-12, 2019, pages 60-71. IEEE Computer Society, 2019. URL: https://doi.org/10.1109/FOCS.2019.00013.
  8. Yossi Azar and Noam Touitou. Beyond tree embeddings - a deterministic framework for network design with deadlines or delay. In 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 1368-1379. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00129.
  9. Ashwinkumar Badanidiyuru, Shahar Dobzinski, Hu Fu, Robert Kleinberg, Noam Nisan, and Tim Roughgarden. Sketching valuation functions. In SODA, pages 1025-1035. SIAM, 2012. Google Scholar
  10. Kshipra Bhawalkar and Tim Roughgarden. Welfare guarantees for combinatorial auctions with item bidding. In SODA, pages 700-709. SIAM, 2011. Google Scholar
  11. Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukáš Folwarczný, Lukasz Jez, Jirí Sgall, Kim Thang Nguyen, and Pavel Veselý. Online algorithms for multilevel aggregation. Oper. Res., 68(1):214-232, 2020. URL: https://doi.org/10.1287/opre.2019.1847.
  12. Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukáš Folwarczný, Lukasz Jez, Jirí Sgall, Kim Thang Nguyen, and Pavel Veselý. New results on multi-level aggregation. Theor. Comput. Sci., 861:133-143, 2021. URL: https://doi.org/10.1016/j.tcs.2021.02.016.
  13. Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, and Jan Marcinkowski. Online facility location with linear delay. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022, September 19-21, 2022, University of Illinois, Urbana-Champaign, USA (Virtual Conference), volume 245 of LIPIcs, pages 45:1-45:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.APPROX/RANDOM.2022.45.
  14. Marcin Bienkowski, Jaroslaw Byrka, Marek Chrobak, Lukasz Jez, Dorian Nogneng, and Jirí Sgall. Better approximation bounds for the joint replenishment problem. In Chandra Chekuri, editor, Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, January 5-7, 2014, pages 42-54. SIAM, 2014. URL: https://doi.org/10.1137/1.9781611973402.4.
  15. Marcin Bienkowski, Artur Kraska, Hsiang-Hsuan Liu, and Pawel Schmidt. A primal-dual online deterministic algorithm for matching with delays. In Approximation and Online Algorithms - Proceedings of the 16th International Workshop, WAOA 2018, Helsinki, Finland, August 23-24, 2018, Revised Selected Papers, volume 11312 of Lecture Notes in Computer Science, pages 51-68. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-04693-4_4.
  16. Marcin Bienkowski, Artur Kraska, and Pawel Schmidt. A match in time saves nine: Deterministic online matching with delays. In Approximation and Online Algorithms - Proceedings of the 15th International Workshop, WAOA 2017, volume 10787 of Lecture Notes in Computer Science, pages 132-146. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-89441-6_11.
  17. Marcin Bienkowski, Artur Kraska, and Pawel Schmidt. Online service with delay on a line. In Zvi Lotker and Boaz Patt-Shamir, editors, Structural Information and Communication Complexity - 25th International Colloquium, SIROCCO 2018, Ma'ale HaHamisha, Israel, June 18-21, 2018, Revised Selected Papers, volume 11085 of Lecture Notes in Computer Science, pages 237-248. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-01325-7_22.
  18. Carlos Fisch Brito, Elias Koutsoupias, and Shailesh Vaya. Competitive analysis of organization networks or multicast acknowledgment: How much to wait? Algorithmica, 64(4):584-605, 2012. URL: https://doi.org/10.1007/s00453-011-9567-5.
  19. Niv Buchbinder, Moran Feldman, Joseph (Seffi) Naor, and Ohad Talmon. O(depth)-competitive algorithm for online multi-level aggregation. In Philip N. Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1235-1244. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.80.
  20. Niv Buchbinder, Kamal Jain, and Joseph Naor. Online primal-dual algorithms for maximizing ad-auctions revenue. In Lars Arge, Michael Hoffmann, and Emo Welzl, editors, Algorithms - ESA 2007, 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007, Proceedings, volume 4698 of Lecture Notes in Computer Science, pages 253-264. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-75520-3_24.
  21. Niv Buchbinder, Tracy Kimbrel, Retsef Levi, Konstantin Makarychev, and Maxim Sviridenko. Online make-to-order joint replenishment model: primal dual competitive algorithms. In Shang-Hua Teng, editor, Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, San Francisco, California, USA, January 20-22, 2008, pages 952-961. SIAM, 2008. URL: http://dl.acm.org/citation.cfm?id=1347082.1347186.
  22. Rodrigo A. Carrasco, Kirk Pruhs, Cliff Stein, and José Verschae. The online set aggregation problem. In Michael A. Bender, Martin Farach-Colton, and Miguel A. Mosteiro, editors, LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Buenos Aires, Argentina, April 16-19, 2018, Proceedings, volume 10807 of Lecture Notes in Computer Science, pages 245-259. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-77404-6_19.
  23. Ryder Chen, Jahanvi Khatkar, and Seeun William Umboh. Online weighted cardinality joint replenishment problem with delay. In Mikolaj Bojanczyk, Emanuela Merelli, and David P. Woodruff, editors, 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4-8, 2022, Paris, France, volume 229 of LIPIcs, pages 40:1-40:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.40.
  24. Lindsey Deryckere and Seeun William Umboh. Online matching with set and concave delays. In Nicole Megow and Adam D. Smith, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023, September 11-13, 2023, Atlanta, Georgia, USA, volume 275 of LIPIcs, pages 17:1-17:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.APPROX/RANDOM.2023.17.
  25. Shahar Dobzinski. Two randomized mechanisms for combinatorial auctions. In APPROX-RANDOM, volume 4627 of Lecture Notes in Computer Science, pages 89-103. Springer, 2007. Google Scholar
  26. Shahar Dobzinski, Uriel Feige, and Michal Feldman. Are gross substitutes a substitute for submodular valuations? In EC, pages 390-408. ACM, 2021. Google Scholar
  27. Daniel R. Dooly, Sally A. Goldman, and Stephen D. Scott. On-line analysis of the TCP acknowledgment delay problem. J. ACM, 48(2):243-273, 2001. URL: https://doi.org/10.1145/375827.375843.
  28. Yuval Emek, Shay Kutten, and Roger Wattenhofer. Online matching: haste makes waste! In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, pages 333-344. ACM, 2016. URL: https://doi.org/10.1145/2897518.2897557.
  29. Yuval Emek, Yaacov Shapiro, and Yuyi Wang. Minimum cost perfect matching with delays for two sources. Theor. Comput. Sci., 754:122-129, 2019. URL: https://doi.org/10.1016/j.tcs.2018.07.004.
  30. Tomer Ezra, Michal Feldman, Tim Roughgarden, and Warut Suksompong. Pricing multi-unit markets. ACM Trans. Economics and Comput., 7(4):20:1-20:29, 2020. Google Scholar
  31. Michel X. Goemans, Nicholas J. A. Harvey, Satoru Iwata, and Vahab S. Mirrokni. Approximating submodular functions everywhere. In SODA, pages 535-544. SIAM, 2009. Google Scholar
  32. Sudipto Guha, Adam Meyerson, and Kamesh Munagala. A constant factor approximation for the single sink edge installation problem. SIAM J. Comput., 38(6):2426-2442, 2009. URL: https://doi.org/10.1137/050643635.
  33. Anupam Gupta, Amit Kumar, and Debmalya Panigrahi. Caching with time windows. In Konstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, and Julia Chuzhoy, editors, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020, Chicago, IL, USA, June 22-26, 2020, pages 1125-1138. ACM, 2020. URL: https://doi.org/10.1145/3357713.3384277.
  34. Anupam Gupta, Amit Kumar, and Debmalya Panigrahi. A hitting set relaxation for dollarkdollar-server and an extension to time-windows. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 504-515. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00057.
  35. Lujun Jia, Guolong Lin, Guevara Noubir, Rajmohan Rajaraman, and Ravi Sundaram. Universal approximations for tsp, steiner tree, and set cover. In Harold N. Gabow and Ronald Fagin, editors, Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22-24, 2005, pages 386-395. ACM, 2005. URL: https://doi.org/10.1145/1060590.1060649.
  36. Anna R. Karlin, Claire Kenyon, and Dana Randall. Dynamic TCP acknowledgement and other stories about e/(e-1). In Jeffrey Scott Vitter, Paul G. Spirakis, and Mihalis Yannakakis, editors, Proceedings on 33rd Annual ACM Symposium on Theory of Computing, July 6-8, 2001, Heraklion, Crete, Greece, pages 502-509. ACM, 2001. URL: https://doi.org/10.1145/380752.380845.
  37. Alexander S. Kelso and Vincent P. Crawford. Job matching, coalition formation, and gross substitutes. Econometrica, 50(6):1483-1504, 1982. Google Scholar
  38. Predrag Krnetic, Darya Melnyk, Yuyi Wang, and Roger Wattenhofer. The k-server problem with delays on the uniform metric space. In Yixin Cao, Siu-Wing Cheng, and Minming Li, editors, 31st International Symposium on Algorithms and Computation, ISAAC 2020, December 14-18, 2020, Hong Kong, China (Virtual Conference), volume 181 of LIPIcs, pages 61:1-61:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2020.61.
  39. Ngoc Mai Le, Seeun William Umboh, and Ningyuan Xie. The power of clairvoyance for multi-level aggregation and set cover with delay. 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 1594-1610. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch59.
  40. Benny Lehmann, Daniel Lehmann, and Noam Nisan. Combinatorial auctions with decreasing marginal utilities. Games Econ. Behav., 55(2):270-296, 2006. Google Scholar
  41. Xingwu Liu, Zhida Pan, Yuyi Wang, and Roger Wattenhofer. Impatient online matching. In Proceedings of the 29th International Symposium on Algorithms and Computation, ISAAC 2018, volume 123 of LIPIcs, pages 62:1-62:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2018.62.
  42. Jeremy McMahan. A d-competitive algorithm for the multilevel aggregation problem with deadlines. CoRR, abs/2108.04422, 2021. URL: https://arxiv.org/abs/2108.04422.
  43. Noam Touitou. Nearly-tight lower bounds for set cover and network design with deadlines/delay. In Hee-Kap Ahn and Kunihiko Sadakane, editors, 32nd International Symposium on Algorithms and Computation, ISAAC 2021, December 6-8, 2021, Fukuoka, Japan, volume 212 of LIPIcs, pages 53:1-53:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2021.53.
  44. Noam Touitou. Frameworks for nonclairvoyant network design with deadlines or delay. In 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023, page to appear, 2023. Google Scholar
  45. Noam Touitou. Improved and deterministic online service with deadlines or delay. In Barna Saha and Rocco A. Servedio, editors, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, FL, USA, June 20-23, 2023, pages 761-774. ACM, 2023. URL: https://doi.org/10.1145/3564246.3585107.
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