Skip to main content
SpringerLink
Log in

More Effort Towards Multiagent Knapsack

  • Conference paper
  • First Online:
SOFSEM 2023: Theory and Practice of Computer Science (SOFSEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13878))

  • 332 Accesses

Abstract

In this paper, we study two multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] studied the model in which each agent expresses its preference by assigning a utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash welfare-based. Informally, diversity is achieved by satisfying as many agents as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of agents, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of agents for the diverse aggregation rule.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Missing details and proofs are present in a longer version of the paper at https://arxiv.org/abs/2208.02766.

References

  1. Anshelevich, E., Bhardwaj, O., Elkind, E., Postl, J., Skowron, P.: Approximating optimal social choice under metric preferences. Artif. Intell. 264, 27–51 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Anshelevich, E., Bhardwaj, O., Postl, J.: Approximating optimal social choice under metric preferences. In: AAAI, pp. 777–783 (2015)

    Google Scholar 

  3. Anshelevich, E., Postl, J.: Randomized social choice functions under metric preferences. J. Artif. Intell. Res. 58(1), 797–827 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Anshelevich, E., Sekar, S.: Blind, greedy, and random: algorithms for matching and clustering using only ordinal information. In: AAAI, pp. 383–389 (2016)

    Google Scholar 

  5. Aziz, H., Lee, B.E.: Proportionally representative participatory budgeting with ordinal preferences. In: AAAI, pp. 5110–5118 (2021)

    Google Scholar 

  6. Aziz, H., Lee, B.E., Talmon, N.: Proportionally representative participatory budgeting: axioms and algorithms. In: AAMAS, pp. 23–31 (2018)

    Google Scholar 

  7. Aziz, H., Shah, N.: Participatory budgeting: models and approaches. In: Rudas, T., Péli, G. (eds.) Pathways Between Social Science and Computational Social Science. CSS, pp. 215–236. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-54936-7_10

    Chapter  Google Scholar 

  8. Benadé, G., Procaccia, A.D., Nath, S., Shah, N.: Preference elicitation for participatory budgeting. Manage. Sci. 67(5), 2813–2827 (2021)

    Article  Google Scholar 

  9. Boutilier, C., Caragiannis, I., Haber, S., Lu, T., Procaccia, A.D., Sheffet, O.: Optimal social choice functions: a utilitarian view. Artif. Intell. 227, 190–213 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bredereck, R., Faliszewski, P., Kaczmarczyk, A., Knop, D., Niedermeier, R.: Parameterized algorithms for finding a collective set of items. In: AAAI, pp. 1838–1845 (2020)

    Google Scholar 

  11. Caragiannis, I., Procaccia, A.D.: Voting almost maximizes social welfare despite limited communication. Artif. Intell. 175(9), 1655–1671 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cygan, M., et al.: Parameterized Algorithms. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3

    Book  MATH  Google Scholar 

  13. Cygan, M., Pilipczuk, M.: Exact and approximate bandwidth. Theoret. Comput. Sci. 411(40–42), 3701–3713 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity, vol. 4. TCS, Springer, London (2013). https://doi.org/10.1007/978-1-4471-5559-1

  15. Elkind, E., Faliszewski, P., Skowron, P., Slinko, A.: Properties of multiwinner voting rules. Soc. Choice Welfare 48(3), 599–632 (2017). https://doi.org/10.1007/s00355-017-1026-z

    Article  MathSciNet  MATH  Google Scholar 

  16. Endriss, U.: Trends in computational social choice. Lulu. com (2017)

    Google Scholar 

  17. Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Committee scoring rules: axiomatic characterization and hierarchy. TEAC 7(1), 1–39 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fluschnik, T., Skowron, P., Triphaus, M., Wilker, K.: Fair knapsack. In: AAAI, pp. 1941–1948 (2019)

    Google Scholar 

  19. Ganuza, E., Baiocchi, G.: The power of ambiguity: how participatory budgeting travels the globe. J. Public Deliberation 8(2), 1–12 (2012)

    Google Scholar 

  20. Goel, A., Krishnaswamy, A.K., Sakshuwong, S., Aitamurto, T.: Knapsack voting for participatory budgeting. ACM Trans. Econ. Comput. 7(2), 1–27 (2019)

    Article  MathSciNet  Google Scholar 

  21. Gupta, S., Jain, P., Panolan, F., Roy, S., Saurabh, S.: Gerrymandering on graphs: computational complexity and parameterized algorithms. In: SAGT, pp. 140–155 (2021)

    Google Scholar 

  22. Gupta, S., Jain, P., Saurabh, S.: Well-structured committees. In: IJCAI, pp. 189–195 (2020)

    Google Scholar 

  23. Gupta, S., Jain, P., Saurabh, S., Talmon, N.: Even more effort towards improved bounds and fixed-parameter tractability for multiwinner rules. In: IJCAI, pp. 217–223 (2021)

    Google Scholar 

  24. Hershkowitz, D.E., Kahng, A., Peters, D., Procaccia, A.D.: District-fair participatory budgeting. In: AAAI, pp. 5464–5471 (2021)

    Google Scholar 

  25. Jain, P., Sornat, K., Talmon, N.: Participatory budgeting with project interactions. In: IJCAI, pp. 386–392 (2020)

    Google Scholar 

  26. Jain, P., Sornat, K., Talmon, N., Zehavi, M.: Participatory budgeting with project groups. In: IJCAI, pp. 276–282 (2021)

    Google Scholar 

  27. Jain, P., Talmon, N., Bulteau, L.: Partition aggregation for participatory budgeting. In: AAMAS, pp. 665–673 (2021)

    Google Scholar 

  28. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack problems. Springer (2010). https://doi.org/10.1007/978-3-540-24777-7

  29. Moenck, R.T.: Practical fast polynomial multiplication. In: SYMSAC86, pp. 136–148 (1976)

    Google Scholar 

  30. Niedermeier, R.: Invitation to Fixed-Parameter algorithms. Oxford University Press (2006)

    Google Scholar 

  31. Pierczyński, G., Skowron, P., Peters, D.: Proportional participatory budgeting with additive utilities. In: Advances in Neural Information Processing Systems 34 (2021)

    Google Scholar 

  32. Procaccia, A.D., Rosenschein, J.S.: The distortion of cardinal preferences in voting. In: Proceedings of the 10th International Conference on Cooperative Information Agents, pp. 317–331. CIA2006 (2006)

    Google Scholar 

  33. Gilman, H.R.: Transformative deliberations: participatory budgeting in the United States. J. Public Deliberation 8(2), 1–20 (2012)

    Google Scholar 

  34. Sintomer, Y., Herzberg, C., Röcke, A.: Participatory budgeting in Europe: potentials and challenges. Int. J. Urban Reg. Res. 32(1), 164–178 (2008)

    Article  Google Scholar 

  35. Skowron, P., Faliszewski, P., Lang, J.: Finding a collective set of items: from proportional multirepresentation to group recommendation. Artif. Intell. 241, 191–216 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  36. Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Oper. Res. Lett. 32(1), 41–43 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  37. Talmon, N., Faliszewski, P.: A framework for approval-based budgeting methods. In: AAAI, pp. 2181–2188 (2019)

    Google Scholar 

  38. Wampler, B.: Participatory budgeting in brazil: contestation, cooperation, and accountability. Penn State Press (2010)

    Google Scholar 

Download references

Acknowledgements

Pallavi Jain received funding from Seed Grant (IITJ/ R &D/2022–23/07). Sushmita Gupta received funding from SERB’s Matrics Grant (MTR/2021/000869). Additionally, both were supported by SERB’S SUPRA Grant (SPR/2021/000860).

Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, HBNI, Chennai, India

    Sushmita Gupta & Sanjay Seetharaman

  2. IIT Jodhpur, Jodhpur, India

    Pallavi Jain

Authors
  1. Sushmita Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pallavi Jain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sanjay Seetharaman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanjay Seetharaman .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Leszek Gąsieniec

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gupta, S., Jain, P., Seetharaman, S. (2023). More Effort Towards Multiagent Knapsack. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-23101-8_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23100-1

  • Online ISBN: 978-3-031-23101-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation