Advertisement

Fairly Allocating Contiguous Blocks of Indivisible Items

  • Warut SuksompongEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10504)

Abstract

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a contiguous block on the line. While allocations satisfying the classical fairness notions of proportionality, envy-freeness, and equitability are not guaranteed to exist even without the contiguity requirement, we show the existence of contiguous allocations satisfying approximate versions of these notions that do not degrade as the number of agents or items increases. We also study the efficiency loss of contiguous allocations due to fairness constraints.

References

  1. 1.
    Alon, N.: Splitting necklaces. Adv. Math. 63(3), 247–253 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aumann, Y., Dombb, Y.: The efficiency of fair division with connected pieces. ACM Trans. Econ. Comput. 3(4), 23 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aumann, Y., Dombb, Y., Hassidim, A.: Computing socially-efficient cake divisions. In: Proceedings of the 12th International Conference on Autonomous Agents and Multiagent Systems, pp. 343–350 (2013)Google Scholar
  4. 4.
    Bárány, I., Grinberg, V.S.: Block partitions of sequences. Isr. J. Math. 206(1), 155–164 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bei, X., Chen, N., Hua, X., Tao, B., Yang, E.: Optimal proportional cake cutting with connected pieces. In: Proceedings of the 26th AAAI Conference on Artificial Intelligence, pp. 1263–1269 (2012)Google Scholar
  6. 6.
    Bilò, V., Fanelli, A., Flammini, M., Monaco, G., Moscardelli, L.: The price of envy-freeness in machine scheduling. Theor. Comput. Sci. 613, 65–78 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bouveret, S., Cechlárová, K., Elkind, E., Igarashi, A., Peters, D.: Fair division of a graph. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence (2017, forthcoming)Google Scholar
  8. 8.
    Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M.: The efficiency of fair division. Theory Comput. Syst. 50, 589–610 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A.D., Shah, N., Wang, J.: The unreasonable fairness of maximum Nash welfare. In: Proceedings of the 17th ACM Conference on Economics and Computation, pp. 305–322 (2016)Google Scholar
  10. 10.
    Cechlárová, K., Doboš, J., Pillárová, E.: On the existence of equitable cake divisions. Inf. Sci. 228, 239–245 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Cohler, Y.J., Lai, J.K., Parkes, D.C., Procaccia, A.D.: Optimal envy-free cake cutting. In: Proceedings of the 25th AAAI Conference on Artificial Intelligence, pp. 626–631 (2011)Google Scholar
  12. 12.
    Dickerson, J.P., Goldman, J., Karp, J., Procaccia, A.D., Sandholm, T.: The computational rise and fall of fairness. In: Proceedings of the 28th AAAI Conference on Artificial Intelligence, pp. 1405–1411 (2014)Google Scholar
  13. 13.
    Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. Am. Math. Mon. 68(1), 1–17 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Heydrich, S., van Stee, R.: Dividing connected chores fairly. Theor. Comput. Sci. 593, 51–61 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lipton, R.J., Markakis, E., Mossel, E., Saberi, A.: On approximately fair allocations of indivisible goods. In: Proceedings of the 5th ACM Conference on Economics and Computation, pp. 125–131 (2004)Google Scholar
  16. 16.
    Manurangsi, P., Suksompong, W.: Asymptotic existence of fair divisions for groups. Math. Soc. Sci. (Forthcoming)Google Scholar
  17. 17.
    Stromquist, W.: How to cut a cake fairly. Am. Math. Mon. 87(8), 640–644 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Stromquist, W.: Envy-free cake divisions cannot be found by finite protocols. Electron. J. Comb. 15, 11 (2008)Google Scholar
  19. 19.
    Su, F.E.: Rental harmony: Sperner’s lemma in fair division. Am. Math. Mon. 106(10), 930–942 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Suksompong, W.: Asymptotic existence of proportionally fair allocations. Math. Soc. Sci. 81, 62–65 (2016)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA

Personalised recommendations