Document Open Access Logo

When Far Is Better: The Chamberlin-Courant Approach to Obnoxious Committee Selection

Authors Sushmita Gupta , Tanmay Inamdar , Pallavi Jain , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

PDF

File

Thumbnail PDF
PDF
LIPIcs.FSTTCS.2024.24.pdf
  • Filesize: 0.98 MB
  • 21 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Fixed parameter tractability
Keywords
  • Metric Space
  • Parameterized Complexity
  • Approximation
  • Obnoxious Facility Location

Metrics

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

Abstract

Classical work on metric space based committee selection problem interprets distance as "near is better". In this work, motivated by real-life situations, we interpret distance as "far is better". Formally stated, we initiate the study of "obnoxious" committee scoring rules when the voters' preferences are expressed via a metric space. To accomplish this, we propose a model where large distances imply high satisfaction (in contrast to the classical setting where shorter distances imply high satisfaction) and study the egalitarian avatar of the well-known Chamberlin-Courant voting rule and some of its generalizations. For a given integer value λ between 1 and k, the committee size, a voter derives satisfaction from only the λth favorite committee member; the goal is to maximize the satisfaction of the least satisfied voter. For the special case of λ = 1, this yields the egalitarian Chamberlin-Courant rule.  In this paper, we consider general metric space and the special case of a d-dimensional Euclidean space. 
We show that when λ is 1 and k, the problem is polynomial-time solvable in ℝ² and general metric space, respectively. However, for λ = k-1, it is NP-hard even in ℝ². Thus, we have "double-dichotomy" in ℝ² with respect to the value of λ, where the extreme cases are solvable in polynomial time but an intermediate case is NP-hard. Furthermore, this phenomenon appears to be "tight" for ℝ² because the problem is NP-hard for general metric space, even for λ = 1. Consequently, we are motivated to explore the problem in the realm of (parameterized) approximation algorithms and obtain positive results. Interestingly, we note that this generalization of Chamberlin-Courant rules encodes practical constraints that are relevant to solutions for certain facility locations.

Cite As Get BibTex

Sushmita Gupta, Tanmay Inamdar, Pallavi Jain, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. When Far Is Better: The Chamberlin-Courant Approach to Obnoxious Committee Selection. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.24

Author Details

Sushmita Gupta
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
Tanmay Inamdar
  • Indian Institute of Technology Jodhpur, Jodhpur, India
Pallavi Jain
  • Indian Institute of Technology Jodhpur, Jodhpur, India
Daniel Lokshtanov
  • University of California Santa Barbara, CA, USA
Fahad Panolan
  • School of Computer Science, University of Leeds, UK
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
  • University of Bergen, Norway

Funding

Sushmita Gupta and Pallavi Jain acknowledge support from SERB-SUPRA (grant number SPR/2021/000860).
  • Gupta, Sushmita: The author acknowledges the support from SERB-MATRICS (grant number MTR/2021/000869).
  • Inamdar, Tanmay: The author acknowledges support from IITJ Research Initiation Grant (grant number I/RIG/TNI/20240072).
  • Jain, Pallavi: The author acknowledges support from IITJ Seed Grant (grant number I/SEED/PJ/ 20210119).
  • Lokshtanov, Daniel: The author acknowledges support from NSF award CCF-2008838.
  • Saurabh, Saket: The author acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416); and he also acknowledges the support of Swarnajayanti Fellowship (grant number DST/SJF/MSA-01/2017-18).

References

  1. Hyung-Chan An and O. Svensson. Recent developments in approximation algorithms for facility location and clustering problems. In Combinatorial Optimization and Graph Algorithms: Communications of NII Shonan Meetings, pages 1-19. Springer, 2017. Google Scholar
  2. Nima Anari, Moses Charikar, and Prasanna Ramakrishnan. Distortion in metric matching with ordinal preferences. In Kevin Leyton-Brown, Jason D. Hartline, and Larry Samuelson, editors, Proceedings of the 24th ACM Conference on Economics and Computation, EC 2023, London, United Kingdom, July 9-12, 2023, pages 90-110. ACM, 2023. URL: https://doi.org/10.1145/3580507.3597740.
  3. Haris Aziz, Felix Brandt, Edith Elkind, and Piotr Skowron. Computational social choice: The first ten years and beyond. In Bernhard Steffen and Gerhard J. Woeginger, editors, Computing and Software Science - State of the Art and Perspectives, volume 10000 of Lecture Notes in Computer Science, pages 48-65. Springer, 2019. URL: https://doi.org/10.1007/978-3-319-91908-9_4.
  4. Haris Aziz, Piotr Faliszewski, Bernard Grofman, Arkadii Slinko, and Nimrod Talmon. Egalitarian committee scoring rules. In Jérôme Lang, editor, Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden, pages 56-62. ijcai.org, 2018. URL: https://doi.org/10.24963/IJCAI.2018/8.
  5. Haris Aziz, Serge Gaspers, Joachim Gudmundsson, Simon Mackenzie, Nicholas Mattei, and Toby Walsh. Computational aspects of multi-winner approval voting. In Gerhard Weiss, Pinar Yolum, Rafael H. Bordini, and Edith Elkind, editors, Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, Istanbul, Turkey, May 4-8, 2015, pages 107-115. ACM, 2015. URL: http://dl.acm.org/citation.cfm?id=2772896.
  6. Nadja Betzler, Robert Bredereck, Jiehua Chen, and Rolf Niedermeier. Studies in computational aspects of voting - A parameterized complexity perspective. In Hans L. Bodlaender, Rod Downey, Fedor V. Fomin, and Dániel Marx, editors, The Multivariate Algorithmic Revolution and Beyond - Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday, volume 7370 of Lecture Notes in Computer Science, pages 318-363. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-30891-8_16.
  7. Nadja Betzler, Arkadii Slinko, and Johannes Uhlmann. On the computation of fully proportional representation. J. Artif. Intell. Res., 47:475-519, 2013. URL: https://doi.org/10.1613/JAIR.3896.
  8. Steven J Brams, D Marc Kilgour, and M Remzi Sanver. A minimax procedure for electing committees. Public Choice, 132:401-420, 2007. Google Scholar
  9. Felix Brandt, Markus Brill, and Bernhard Harrenstein. Tournament Solutions. In F Brandt, V Conitzer, U Endriss, J Lang, and A. D. Procaccia, editors, Handbook of Computational Social Choice, pages 453-474. Cambridge University Press, 2016. Google Scholar
  10. Robert Bredereck, Piotr Faliszewski, Andrzej Kaczmarczyk, Dusan Knop, and Rolf Niedermeier. Parameterized algorithms for finding a collective set of items. In The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7-12, 2020, pages 1838-1845. AAAI Press, 2020. URL: https://doi.org/10.1609/AAAI.V34I02.5551.
  11. Robert Bredereck, Piotr Faliszewski, Andrzej Kaczmarczyk, Rolf Niedermeier, Piotr Skowron, and Nimrod Talmon. Robustness among multiwinner voting rules. Artif. Intell., 290:103403, 2021. URL: https://doi.org/10.1016/J.ARTINT.2020.103403.
  12. Markus Brill, Piotr Faliszewski, Frank Sommer, and Nimrod Talmon. Approximation algorithms for balancedcc multiwinner rules. In AAMAS '19, pages 494-502, 2019. URL: http://dl.acm.org/citation.cfm?id=3331732.
  13. Laurent Bulteau, Gal Shahaf, Ehud Shapiro, and Nimrod Talmon. Aggregation over metric spaces: Proposing and voting in elections, budgeting, and legislation. J. Artif. Intell. Res., 70:1413-1439, 2021. URL: https://doi.org/10.1613/JAIR.1.12388.
  14. Deeparnab Chakrabarty, Luc Côté, and Ankita Sarkar. Fault-tolerant k-supplier with outliers. In Olaf Beyersdorff, Mamadou Moustapha Kanté, Orna Kupferman, and Daniel Lokshtanov, editors, 41st International Symposium on Theoretical Aspects of Computer Science, STACS 2024, March 12-14, 2024, Clermont-Ferrand, France, volume 289 of LIPIcs, pages 23:1-23:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPICS.STACS.2024.23.
  15. Deeparnab Chakrabarty and Chaitanya Swamy. Interpolating between k-median and k-center: Approximation algorithms for ordered k-median. In Ioannis Chatzigiannakis, Christos Kaklamanis, Dániel Marx, and Donald Sannella, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, volume 107 of LIPIcs, pages 29:1-29:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPICS.ICALP.2018.29.
  16. John R Chamberlin and Paul N Courant. Representative deliberations and representative decisions: Proportional representation and the borda rule. American Political Science Review, 77(3):718-733, 1983. Google Scholar
  17. Hau Chan, Aris Filos-Ratsikas, Bo Li, Minming Li, and Chenhao Wang. Mechanism design for facility location problems: A survey. In Proceedings of IJCAI, pages 4356-4365, 2021. URL: https://doi.org/10.24963/IJCAI.2021/596.
  18. Moses Charikar, Kangning Wang, Prasanna Ramakrishnan, and Hongxun Wu. Breaking the metric voting distortion barrier. In David P. Woodruff, editor, Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024, pages 1621-1640. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.65.
  19. Shiri Chechik and David Peleg. The fault-tolerant capacitated k-center problem. Theor. Comput. Sci., 566:12-25, 2015. URL: https://doi.org/10.1016/J.TCS.2014.11.017.
  20. Jiehua Chen and Sven Grottke. Small one-dimensional euclidean preference profiles. Soc. Choice Welf., 57(1):117-144, 2021. URL: https://doi.org/10.1007/S00355-020-01301-Y.
  21. Richard L Church and Zvi Drezner. Review of obnoxious facilities location problems. Comput. Oper. Res., 138:105468, 2022. URL: https://doi.org/10.1016/J.COR.2021.105468.
  22. Vincent Cohen-Addad, Fabrizio Grandoni, Euiwoong Lee, and Chris Schwiegelshohn. Breaching the 2 LMP approximation barrier for facility location with applications to k-median. In Proceedings of SODA, pages 940-986, 2023. URL: https://doi.org/10.1137/1.9781611977554.CH37.
  23. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  24. Eva Michelle Deltl, Till Fluschnik, and Robert Bredereck. Algorithmics of egalitarian versus equitable sequences of committees. In IJCAI 2023, pages 2651-2658, 2023. URL: https://doi.org/10.24963/IJCAI.2023/295.
  25. Robert G. Downey and Michael R. Fellows. Fundamentals of parameterized complexity, volume 4. Springer, 2013. Google Scholar
  26. Herbert Edelsbrunner and Ernst P. Mücke. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph., 9(1):66-104, 1990. URL: https://doi.org/10.1145/77635.77639.
  27. Edith Elkind, Piotr Faliszewski, Jean-François Laslier, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. What do multiwinner voting rules do? an experiment over the two-dimensional euclidean domain. In Satinder Singh and Shaul Markovitch, editors, Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, San Francisco, California, USA, pages 494-501. AAAI Press, 2017. URL: https://doi.org/10.1609/AAAI.V31I1.10612.
  28. Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Multiwinner rules on paths from k-borda to chamberlin-courant. In Carles Sierra, editor, Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017, pages 192-198. ijcai.org, 2017. URL: https://doi.org/10.24963/IJCAI.2017/28.
  29. Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Multiwinner voting: A new challenge for social choice theory. Trends in computational social choice, 74(2017):27-47, 2017. Google Scholar
  30. Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives. Soc. Choice Welf., 51(3):513-550, 2018. URL: https://doi.org/10.1007/S00355-018-1126-4.
  31. Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Committee scoring rules: Axiomatic characterization and hierarchy. ACM Trans. Economics and Comput., 7(1):3:1-3:39, 2019. URL: https://doi.org/10.1145/3296672.
  32. Piotr Faliszewski, Piotr Skowron, and Nimrod Talmon. Bribery as a measure of candidate success: Complexity results for approval-based multiwinner rules. In Kate Larson, Michael Winikoff, Sanmay Das, and Edmund H. Durfee, editors, Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, AAMAS 2017, São Paulo, Brazil, May 8-12, 2017, pages 6-14. ACM, 2017. URL: http://dl.acm.org/citation.cfm?id=3091133.
  33. Jörg Flum and Martin Grohe. Parameterized Complexity Theory. Springer, 2006. URL: https://doi.org/10.1007/3-540-29953-X.
  34. Michal Tomasz Godziszewski, Pawel Batko, Piotr Skowron, and Piotr Faliszewski. An analysis of approval-based committee rules for 2d-euclidean elections. In Proceedings of AAAI, pages 5448-5455, 2021. URL: https://doi.org/10.1609/AAAI.V35I6.16686.
  35. Kishen N. Gowda, Thomas W. Pensyl, Aravind Srinivasan, and Khoa Trinh. Improved bi-point rounding algorithms and a golden barrier for k-median. In Proceedings of SODA, pages 987-1011, 2023. URL: https://doi.org/10.1137/1.9781611977554.CH38.
  36. Sushmita Gupta, Tanmay Inamdar, Pallavi Jain, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. When far is better: The chamberlin-courant approach to obnoxious committee selection. CoRR, abs/2405.15372, 2024. URL: https://doi.org/10.48550/arXiv.2405.15372.
  37. Sushmita Gupta, Pallavi Jain, Saket Saurabh, and Nimrod Talmon. Even more effort towards improved bounds and fixed-parameter tractability for multiwinner rules. In Proceedings of IJCAI, pages 217-223, 2021. URL: https://doi.org/10.24963/IJCAI.2021/31.
  38. Aviram Imber, Jonas Israel, Markus Brill, Hadas Shachnai, and Benny Kimelfeld. Spatial voting with incomplete voter information. In AAAI 2024, pages 9790-9797, 2024. URL: https://doi.org/10.1609/AAAI.V38I9.28838.
  39. Tanmay Inamdar and Kasturi R. Varadarajan. Fault tolerant clustering with outliers. In Evripidis Bampis and Nicole Megow, editors, Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Munich, Germany, September 12-13, 2019, Revised Selected Papers, volume 11926 of Lecture Notes in Computer Science, pages 188-201. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-39479-0_13.
  40. Sangram Kishor Jena, Ramesh K. Jallu, Gautam K. Das, and Subhas C. Nandy. The maximum distance-d independent set problem on unit disk graphs. In Jianer Chen and Pinyan Lu, editors, Frontiers in Algorithmics - 12th International Workshop, FAW 2018, Guangzhou, China, May 8-10, 2018, Proceedings, volume 10823 of Lecture Notes in Computer Science, pages 68-80. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-78455-7_6.
  41. Yusuf Hakan Kalayci, David Kempe, and Vikram Kher. Proportional representation in metric spaces and low-distortion committee selection. In AAAI 2024, pages 9815-9823, 2024. URL: https://doi.org/10.1609/AAAI.V38I9.28841.
  42. Richard M. Karp. Reducibility among combinatorial problems. In Raymond E. Miller and James W. Thatcher, editors, Proceedings of CCC, pages 85-103, 1972. URL: https://doi.org/10.1007/978-1-4684-2001-2_9.
  43. Samir Khuller, Robert Pless, and Yoram J. Sussmann. Fault tolerant k-center problems. Theor. Comput. Sci., 242(1-2):237-245, 2000. URL: https://doi.org/10.1016/S0304-3975(98)00222-9.
  44. Steven Klein. On the egalitarian value of electoral democracy. Political Theory, page 00905917231217133, 2023. Google Scholar
  45. Nirman Kumar and Benjamin Raichel. Fault tolerant clustering revisited. In Proceedings of the 25th Canadian Conference on Computational Geometry, CCCG 2013, Waterloo, Ontario, Canada, August 8-10, 2013. Carleton University, Ottawa, Canada, 2013. URL: http://cccg.ca/proceedings/2013/papers/paper_36.pdf.
  46. Martin Lackner and Piotr Skowron. Multi-winner voting with approval preferences. Springer Nature, 2023. Google Scholar
  47. Alexander Lam, Haris Aziz, Bo Li, Fahimeh Ramezani, and Toby Walsh. Proportional fairness in obnoxious facility location. In Mehdi Dastani, Jaime Simão Sichman, Natasha Alechina, and Virginia Dignum, editors, Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2024, Auckland, New Zealand, May 6-10, 2024, pages 1075-1083. International Foundation for Autonomous Agents and Multiagent Systems / ACM, 2024. URL: https://doi.org/10.5555/3635637.3662963.
  48. Jean-François Laslier. Spatial approval voting. Political Analysis, 14(2):160-185, 2006. Google Scholar
  49. Hong Liu and Jiong Guo. Parameterized complexity of winner determination in minimax committee elections. In Catholijn M. Jonker, Stacy Marsella, John Thangarajah, and Karl Tuyls, editors, Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems, Singapore, May 9-13, 2016, pages 341-349. ACM, 2016. URL: http://dl.acm.org/citation.cfm?id=2936975.
  50. Jirí Matousek. Lectures on discrete geometry, volume 212 of Graduate texts in mathematics. Springer, 2002. Google Scholar
  51. Ivan-Aleksandar Mavrov, Kamesh Munagala, and Yiheng Shen. Fair multiwinner elections with allocation constraints. In Proceedings of EC, pages 964-990, 2023. URL: https://doi.org/10.1145/3580507.3597685.
  52. Neeldhara Misra, Arshed Nabeel, and Harman Singh. On the parameterized complexity of minimax approval voting. In Gerhard Weiss, Pinar Yolum, Rafael H. Bordini, and Edith Elkind, editors, Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, Istanbul, Turkey, May 4-8, 2015, pages 97-105. ACM, 2015. URL: http://dl.acm.org/citation.cfm?id=2772895.
  53. Burt L Monroe. Fully proportional representation. American Political Science Review, 89(4):925-940, 1995. Google Scholar
  54. Kamesh Munagala, Yiheng Shen, Kangning Wang, and Zhiyi Wang. Approximate core for committee selection via multilinear extension and market clearing. In Proceedings of SODA, pages 2229-2252, 2022. URL: https://doi.org/10.1137/1.9781611977073.89.
  55. Kamesh Munagala, Zeyu Shen, and Kangning Wang. Optimal algorithms for multiwinner elections and the chamberlin-courant rule. In EC '21, pages 697-717. ACM, 2021. URL: https://doi.org/10.1145/3465456.3467624.
  56. Rolf Niedermeier. Invitation to Fixed-Parameter Algorithms. Oxford University Press, 2006. URL: https://doi.org/10.1093/ACPROF:OSO/9780198566076.001.0001.
  57. Sridhar Rajagopalan and Vijay V. Vazirani. Primal-dual RNC approximation algorithms for set cover and covering integer programs. SIAM J. Comput., 28(2):525-540, 1998. URL: https://doi.org/10.1137/S0097539793260763.
  58. John Rawls. A Theory of Justice: Original Edition. Harvard University Press, 1971. URL: http://www.jstor.org/stable/j.ctvjf9z6v.
  59. John Rawls. Justice as Fairness: Political Not Metaphysical, pages 145-173. Palgrave Macmillan UK, London, 1991. URL: https://doi.org/10.1007/978-1-349-21763-2_10.
  60. Piotr Skowron. FPT approximation schemes for maximizing submodular functions. Inf. Comput., 257:65-78, 2017. URL: https://doi.org/10.1016/J.IC.2017.10.002.
  61. Piotr Skowron and Piotr Faliszewski. Chamberlin-courant rule with approval ballots: Approximating the maxcover problem with bounded frequencies in FPT time. J. Artif. Intell. Res., 60:687-716, 2017. URL: https://doi.org/10.1613/JAIR.5628.
  62. Piotr Skowron, Piotr Faliszewski, and Jérôme Lang. Finding a collective set of items: From proportional multirepresentation to group recommendation. Artif. Intell., 241:191-216, 2016. URL: https://doi.org/10.1016/J.ARTINT.2016.09.003.
  63. Piotr Krzysztof Skowron and Edith Elkind. Social choice under metric preferences: Scoring rules and STV. In Proceedings of AAAI, pages 706-712. AAAI Press, 2017. URL: https://doi.org/10.1609/AAAI.V31I1.10591.
  64. Chinmay Sonar, Subhash Suri, and Jie Xue. Multiwinner elections under minimax chamberlin-courant rule in euclidean space. In Proceedings of IJCAI, pages 475-481, 2022. URL: https://doi.org/10.24963/IJCAI.2022/68.
  65. Chinmay Sonar, Subhash Suri, and Jie Xue. Fault tolerance in euclidean committee selection. In ESA 2023, volume 274, pages 95:1-95:14, 2023. URL: https://doi.org/10.4230/LIPICS.ESA.2023.95.
  66. Gogulapati Sreedurga, Mayank Ratan Bhardwaj, and Yadati Narahari. Maxmin participatory budgeting. In IJCAI 2022, pages 489-495, 2022. URL: https://doi.org/10.24963/IJCAI.2022/70.
  67. Arie Tamir. Obnoxious facility location on graphs. SIAM J. Discret. Math., 4(4):550-567, 1991. URL: https://doi.org/10.1137/0404048.
  68. Thorvald N. Thiele. Om flerfoldsvalg. Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger, pages 415-441, 1895. Google Scholar
  69. Yongjie Yang. On the complexity of calculating approval-based winners in candidates-embedded metrics. In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI-22, pages 585-591, 2022. URL: https://doi.org/10.24963/IJCAI.2022/83.
  70. Yongjie Yang and Jianxin Wang. Parameterized complexity of multi-winner determination: More effort towards fixed-parameter tractability. In Elisabeth André, Sven Koenig, Mehdi Dastani, and Gita Sukthankar, editors, Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS 2018, Stockholm, Sweden, July 10-15, 2018, pages 2142-2144. International Foundation for Autonomous Agents and Multiagent Systems Richland, SC, USA / ACM, 2018. URL: http://dl.acm.org/citation.cfm?id=3238099.
  71. Vikram Kher Yusuf Hakan Kalayci, David Kempe. Proportional representation in metric spaces and low-distortion committee selection. In Proceedings of AAAI, 2024. Google Scholar
  72. Aizhong Zhou, Yongjie Yang, and Jiong Guo. Parameterized complexity of committee elections with dichotomous and trichotomous votes. In Edith Elkind, Manuela Veloso, Noa Agmon, and Matthew E. Taylor, editors, Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS '19, Montreal, QC, Canada, May 13-17, 2019, pages 503-510. International Foundation for Autonomous Agents and Multiagent Systems, 2019. URL: http://dl.acm.org/citation.cfm?id=3331733.
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