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The Communication Complexity of Combinatorial Auctions in Graphs

Authors George Christodoulou , Elias Koutsoupias , Annamária Kovács , Ioannis Vlachos

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Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Computational pricing and auctions
  • Theory of computation → Communication complexity
Keywords
  • Auctions
  • Communication Complexity
  • Mechanism Design
  • Graphs

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Abstract

We study truthful and non-truthful protocols for combinatorial auctions in which every item can be allocated to one of two agents (multigraphs), or more generally to a fixed number of agents (hypergraphs). We show some tight - both positive and impossibility - results for the communication complexity of approximating the optimal social welfare for general monotone, subadditive, or XOS valuations.

Cite As Get BibTex

George Christodoulou, Elias Koutsoupias, Annamária Kovács, and Ioannis Vlachos. The Communication Complexity of Combinatorial Auctions in Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.27

Author Details

George Christodoulou
  • Aristotle University of Thessaloniki, Greece
  • Archimedes, Athena Research Center, Greece
Elias Koutsoupias
  • University of Oxford, UK
Annamária Kovács
  • Goethe University, Frankfurt am Main, Germany
Ioannis Vlachos
  • Athens University of Economics and Business, Greece
  • Archimedes, Athena Research Center, Greece

Funding

George Christodoulou, Ioannis Vlachos: This work has been partially supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.

Acknowledgements

We would like to thank an anonymous reviewer for suggesting a refined analysis of an earlier version of the proof in Theorem 8, which helped us obtain the tight bound presented in the current version.

References

  1. Noga Alon, Yossi Matias, and Mario Szegedy. The space complexity of approximating the frequency moments. J. Comput. Syst. Sci., 58(1):137-147, 1999. URL: https://doi.org/10.1006/JCSS.1997.1545.
  2. Georgios Amanatidis, Aris Filos-Ratsikas, and Alkmini Sgouritsa. Pushing the frontier on approximate EFX allocations. In EC, pages 1268-1286. ACM, 2024. URL: https://doi.org/10.1145/3670865.3673582.
  3. Yuichi Asahiro, Jesper Jansson, Eiji Miyano, and Hirotaka Ono. Graph orientation to maximize the minimum weighted outdegree. Int. J. Found. Comput. Sci., 22(3):583-601, 2011. URL: https://doi.org/10.1142/S0129054111008246.
  4. Yuichi Asahiro, Eiji Miyano, and Hirotaka Ono. Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree. Discret. Appl. Math., 159(7):498-508, 2011. URL: https://doi.org/10.1016/J.DAM.2010.11.003.
  5. Sepehr Assadi, Thomas Kesselheim, and Sahil Singla. Improved truthful mechanisms for subadditive combinatorial auctions: Breaking the logarithmic barrier. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 653-661. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.40.
  6. Sepehr Assadi, Hrishikesh Khandeparkar, Raghuvansh R. Saxena, and S. Matthew Weinberg. Separating the communication complexity of truthful and nontruthful algorithms for combinatorial auctions. SIAM J. Comput., 51(3):20-75, 2022. URL: https://doi.org/10.1137/20M1370021.
  7. Liad Blumrosen and Noam Nisan. On the computational power of iterative auctions. In EC, pages 29-43. ACM, 2005. URL: https://doi.org/10.1145/1064009.1064013.
  8. Hans L. Bodlaender. Dynamic programming on graphs with bounded treewidth. In Timo Lepistö and Arto Salomaa, editors, Automata, Languages and Programming, pages 105-118, Berlin, Heidelberg, 1988. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/3-540-19488-6_110.
  9. Dave Buchfuhrer, Shaddin Dughmi, Hu Fu, Robert Kleinberg, Elchanan Mossel, Christos Papadimitriou, Michael Schapira, Yaron Singer, and Chris Umans. Inapproximability for vcg-based combinatorial auctions. In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 518-536. SIAM, 2010. Google Scholar
  10. George Christodoulou, Amos Fiat, Elias Koutsoupias, and Alkmini Sgouritsa. Fair allocation in graphs. In Proceedings of the 24th ACM Conference on Economics and Computation, pages 473-488, 2023. URL: https://doi.org/10.1145/3580507.3597764.
  11. George Christodoulou, Elias Koutsoupias, and Annamária Kovács. Truthful allocation in graphs and hypergraphs. In ICALP, volume 198 of LIPIcs, pages 56:1-56:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.56.
  12. George Christodoulou, Elias Koutsoupias, and Annamária Kovács. A proof of the Nisan-Ronen conjecture. In STOC, pages 672-685. ACM, 2023. URL: https://doi.org/10.1145/3564246.3585176.
  13. Edward H Clarke. Multipart pricing of public goods. Public choice, pages 17-33, 1971. Google Scholar
  14. Amit Daniely, Michael Schapira, and Gal Shahaf. Inapproximability of truthful mechanisms via generalizations of the vc dimension. In Proceedings of the forty-seventh annual ACM symposium on Theory of Computing, pages 401-408, 2015. URL: https://doi.org/10.1145/2746539.2746597.
  15. Shahar Dobzinski. Two randomized mechanisms for combinatorial auctions. In International Workshop on Approximation Algorithms for Combinatorial Optimization, pages 89-103. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74208-1_7.
  16. Shahar Dobzinski. Computational efficiency requires simple taxation. In FOCS, pages 209-218. IEEE Computer Society, 2016. URL: https://doi.org/10.1109/FOCS.2016.30.
  17. Shahar Dobzinski and Noam Nisan. Limitations of vcg-based mechanisms. Comb., 31(4):379-396, 2011. URL: https://doi.org/10.1007/S00493-011-2528-4.
  18. Shahar Dobzinski, Noam Nisan, and Michael Schapira. Approximation algorithms for combinatorial auctions with complement-free bidders. In Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, pages 610-618, 2005. URL: https://doi.org/10.1145/1060590.1060681.
  19. Shahar Dobzinski, Noam Nisan, and Michael Schapira. Truthful randomized mechanisms for combinatorial auctions. In Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pages 644-652, 2006. URL: https://doi.org/10.1145/1132516.1132607.
  20. Shahar Dobzinski and Michael Schapira. An improved approximation algorithm for combinatorial auctions with submodular bidders. In Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pages 1064-1073, 2006. URL: http://dl.acm.org/citation.cfm?id=1109557.1109675.
  21. Shahar Dobzinski and Jan Vondrák. The computational complexity of truthfulness in combinatorial auctions. In EC, pages 405-422. ACM, 2012. URL: https://doi.org/10.1145/2229012.2229044.
  22. Shahar Dobzinski and Jan Vondrák. From query complexity to computational complexity. In Proceedings of the forty-fourth annual ACM symposium on Theory of computing, pages 1107-1116, 2012. URL: https://doi.org/10.1145/2213977.2214076.
  23. Shahar Dobzinski and Jan Vondrák. Impossibility results for truthful combinatorial auctions with submodular valuations. J. ACM, 63(1):5:1-5:19, 2016. URL: https://doi.org/10.1145/2786754.
  24. Tomás Ebenlendr, Marek Krcál, and Jirí Sgall. Graph balancing: A special case of scheduling unrelated parallel machines. Algorithmica, 68(1):62-80, 2014. URL: https://doi.org/10.1007/S00453-012-9668-9.
  25. Paul Erdős and András Hajnal. On chromatic number of graphs and set-systems. Acta Math. Acad. Sci. Hungar, 17(61-99):1, 1966. Google Scholar
  26. Uriel Feige. On maximizing welfare when utility functions are subadditive. In Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pages 41-50, 2006. URL: https://doi.org/10.1145/1132516.1132523.
  27. Uriel Feige and Jan Vondrák. Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e. In FOCS, pages 667-676. IEEE Computer Society, 2006. URL: https://doi.org/10.1109/FOCS.2006.14.
  28. Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, pages 617-631, 1973. Google Scholar
  29. Ron Holzman, Noa Kfir-Dahav, Dov Monderer, and Moshe Tennenholtz. Bundling equilibrium in combinatorial auctions. Games and Economic Behavior, 47(1):104-123, 2004. URL: https://doi.org/10.1016/S0899-8256(03)00184-2.
  30. Alireza Kaviani, Masoud Seddighin, and AmirMohammad Shahrezaei. Almost envy-free allocation of indivisible goods: A tale of two valuations. arXiv preprint arXiv:2407.05139, 2024. URL: https://doi.org/10.48550/arXiv.2407.05139.
  31. Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, 1997. Google Scholar
  32. Ron Lavi and Chaitanya Swamy. Truthful and near-optimal mechanism design via linear programming. Journal of the ACM (JACM), 58(6):1-24, 2011. URL: https://doi.org/10.1145/2049697.2049699.
  33. Kangbok Lee, Joseph Y.-T. Leung, and Michael L. Pinedo. A note on graph balancing problems with restrictions. Inf. Process. Lett., 110(1):24-29, 2009. URL: https://doi.org/10.1016/J.IPL.2009.09.015.
  34. Noam Nisan and Ilya Segal. The communication requirements of efficient allocations and supporting prices. J. Econ. Theory, 129(1):192-224, 2006. URL: https://doi.org/10.1016/J.JET.2004.10.007.
  35. Christos Papadimitriou, Michael Schapira, and Yaron Singer. On the hardness of being truthful. In 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pages 250-259. IEEE, 2008. URL: https://doi.org/10.1109/FOCS.2008.54.
  36. Frederick V. Qiu and S. Matthew Weinberg. Settling the communication complexity of vcg-based mechanisms for all approximation guarantees. In STOC, pages 1192-1203. ACM, 2024. URL: https://doi.org/10.1145/3618260.3649706.
  37. Shiri Ron, Clayton Thomas, S. Matthew Weinberg, and Qianfan Zhang. Communication separations for truthful auctions: Breaking the two-player barrier. In FOCS, pages 386-405. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00032.
  38. Donald J Rose. On simple characterizations of k-trees. Discrete mathematics, 7(3-4):317-322, 1974. URL: https://doi.org/10.1016/0012-365X(74)90042-9.
  39. José Verschae and Andreas Wiese. On the configuration-lp for scheduling on unrelated machines. J. Sched., 17(4):371-383, 2014. URL: https://doi.org/10.1007/S10951-013-0359-4.
  40. William Vickrey. Counterspeculation, auctions, and competitive sealed tenders. The Journal of finance, 16(1):8-37, 1961. Google Scholar
  41. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of the eleventh annual ACM symposium on Theory of computing, pages 209-213, 1979. URL: https://doi.org/10.1145/800135.804414.
  42. Jinghan A Zeng and Ruta Mehta. On the structure of envy-free orientations on graphs. arXiv preprint arXiv:2404.13527, 2024. URL: https://doi.org/10.48550/arXiv.2404.13527.
  43. Yu Zhou, Tianze Wei, Minming Li, and Bo Li. A complete landscape of EFX allocations on graphs: Goods, chores and mixed manna. In IJCAI, pages 3049-3056. ijcai.org, 2024. URL: https://www.ijcai.org/proceedings/2024/338.
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