Tradeoffs Between Information and Ordinal Approximation for Bipartite Matching

  • Elliot Anshelevich
  • Wennan ZhuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10504)


We study ordinal approximation algorithms for maximum-weight bipartite matchings. Such algorithms only know the ordinal preferences of the agents/nodes in the graph for their preferred matches, but must compete with fully omniscient algorithms which know the true numerical edge weights (utilities). Ordinal approximation is all about being able to produce good results with only limited information. Because of this, one important question is how much better the algorithms can be as the amount of information increases. To address this question for forming high-utility matchings between agents in \(\mathcal {X}\) and \(\mathcal {Y}\), we consider three ordinal information types: when we know the preference order of only nodes in \(\mathcal {X}\) for nodes in \(\mathcal {Y}\), when we know the preferences of both \(\mathcal {X}\) and \(\mathcal {Y}\), and when we know the total order of the edge weights in the entire graph, although not the weights themselves. We also consider settings where only the top preferences of the agents are known to us, instead of their full preference orderings. We design new ordinal approximation algorithms for each of these settings, and quantify how well such algorithms perform as the amount of information given to them increases.


  1. 1.
    Abdulkadiroğlu, A., Sönmez, T.: Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66(3), 689–701 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Abraham, D.J., Irving, R.W., Kavitha, T., Mehlhorn, K.: Popular matchings. SIAM J. Comput. 37(4), 1030–1045 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Anshelevich, E., Bhardwaj, O., Postl, J.: Approximating optimal social choice under metric preferences. In: AAAI (2015)Google Scholar
  4. 4.
    Anshelevich, E., Sekar, S.: Blind, greedy, and random: algorithms for matching and clustering using only ordinal information. In: AAAI (2016)Google Scholar
  5. 5.
    Anshelevich, E., Sekar, S.: Truthful mechanisms for matching and clustering in an ordinal world. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 265–278. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-54110-4_19CrossRefzbMATHGoogle Scholar
  6. 6.
    Bhalgat, A., Chakrabarty, D., Khanna, S.: Social welfare in one-sided matching markets without money. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds.) APPROX/RANDOM -2011. LNCS, vol. 6845, pp. 87–98. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22935-0_8CrossRefGoogle Scholar
  7. 7.
    Caragiannis, I., Filos-Ratsikas, A., Frederiksen, S.K.S., Hansen, K.A., Tan, Z.: Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorship. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 236–250. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-54110-4_17CrossRefGoogle Scholar
  8. 8.
    Chakrabarty, D., Swamy, C.: Welfare maximization and truthfulness in mechanism design with ordinal preferences. In: ITCS (2014)Google Scholar
  9. 9.
    Christodoulou, G., Filos-Ratsikas, A., Frederiksen, S.K.S., Goldberg, P.W., Zhang, J., Zhang, J.: Social welfare in one-sided matching mechanisms. In: Osman, N., Sierra, C. (eds.) AAMAS 2016. LNCS (LNAI), vol. 10002, pp. 30–50. Springer, Cham (2016). doi: 10.1007/978-3-319-46882-2_3CrossRefGoogle Scholar
  10. 10.
    Feldman, M., Fiat, A., Golomb, I.: On voting and facility location. In: EC (2016)Google Scholar
  11. 11.
    Filos-Ratsikas, A., Frederiksen, S.K.S., Zhang, J.: Social welfare in one-sided matchings: random priority and beyond. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 1–12. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44803-8_1CrossRefGoogle Scholar
  12. 12.
    Goel, A., Krishnaswamy, A.K., Munagala, K.: Metric distortion of social choice rules: lower bounds and fairness properties. In: EC (2017)Google Scholar
  13. 13.
    Kalyanasundaram, B., Pruhs, K.: On-line weighted matching. In: SODA, vol. 91, pp. 234–240 (1991)Google Scholar
  14. 14.
    Krysta, P., Manlove, D., Rastegari, B., Zhang, J.: Size versus truthfulness in the house allocation problem. In: EC (2014)Google Scholar
  15. 15.
    Rastegari, B., Condon, A., Immorlica, N., Leyton-Brown, K.: Two-sided matching with partial information. In: EC (2013)Google Scholar
  16. 16.
    Roth, A.E., Sotomayor, M.: Two-sided matching. Handb. Game Theory Econ. Appl. 1, 485–541 (1992)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Skowron, P., Elkind, E.: Social choice under metric preferences: scoring rules and STV. In: AAAI (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Rensselaer Polytechnic InstituteTroyUSA

Personalised recommendations