Advertisement

The VLDB Journal

, Volume 28, Issue 2, pp 221–241 | Cite as

A unified agent-based framework for constrained graph partitioning

  • Lefteris Ntaflos
  • George Trimponias
  • Dimitris PapadiasEmail author
Regular Paper
  • 87 Downloads

Abstract

Social networks offer various services such as recommendations of social events, or delivery of targeted advertising material to certain users. In this work, we focus on a specific type of services modeled as constrained graph partitioning (CGP). CGP assigns users of a social network to a set of classes with bounded capacities so that the similarity and the social costs are minimized. The similarity cost is proportional to the dissimilarity between a user and his class, whereas the social cost is measured in terms of friends that are assigned to different classes. In this work, we investigate two solutions for CGP. The first utilizes a game-theoretic framework, where each user constitutes a player that wishes to minimize his own social and similarity cost. The second employs local search, and aims at minimizing the global cost. We show that the two approaches can be unified under a common agent-based framework that allows for two types of deviations. In a unilateral deviation, an agent switches to a new class, whereas in a bilateral deviation a pair of agents exchange their classes. We develop a number of optimization techniques to improve result quality and facilitate efficiency. Our experimental evaluation on real datasets demonstrates that the proposed methods always outperform the state of the art in terms of solution quality, while they are up to an order of magnitude faster.

Keywords

Constrained graph partitioning Game theory Local search 

Notes

Funding

This work was supported by GRF grants 16207914 and 16231216 from Hong Kong RGC.

References

  1. 1.
    Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization, 1st edn. Wiley, Hoboken (1997)zbMATHGoogle Scholar
  2. 2.
    Agarwala, A., Dontcheva, M., Agrawala, M., Drucker, S., Colburn, A., Curless, B., Salesin, D., Cohen, M.: Interactive digital photo-montage. ACM Trans. Graph. 23(3), 294–302 (2004)CrossRefGoogle Scholar
  3. 3.
    Andrews, M., Hajiaghayi, M.T., Karloff, H., Moitra, A.: Capacitated metric labeling. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 11, SIAM, pp. 976–995 (2011)Google Scholar
  4. 4.
    Anshelevich, E., Sekar, S.: Approximate equilibrium and incentivizing social coordination. CoRR arXiv:1404.4718 (2014)
  5. 5.
    Armenatzoglou, N., Pham, H., Ntranos, V., Papadias, D., Shahabi, C.: Real-time multi-criteria social graph partitioning: a game theoretic approach. In: SIGMOD (2015)Google Scholar
  6. 6.
    Barnard, S.: Stochastic stereo matching over scale. Int. J. Comput. Vis. 3(1), 17–32 (1989)CrossRefGoogle Scholar
  7. 7.
    Boykov, Y., Jolly, M.P.: Interactive graph cuts for optimal boundary and region segmentation of objects in N–D images. In: Proceedings of Eighth IEEE International Conference on Computer Vision, vol. 1, pp. 105–112 (2001)Google Scholar
  8. 8.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. PAMI 23(11), 1222–1239 (2001)CrossRefGoogle Scholar
  9. 9.
    Calinescu, G., Karloff, H., Rabani, Y.: Improved approximation algorithms for multiway cut. In: Proceedings of the ACM Symposium on Theory of Computing, ACM (1998)Google Scholar
  10. 10.
    Feldman, M., Friedler, O.: A unified framework for strong price of anarchy in clustering games. In: Proceedings of the 42nd International Colloquium on Automata, Languages, and Programming, Part II, Springer International Publishing, Lecture Notes in Computer Science, vol. 9135, pp. 601–613 (2015)Google Scholar
  11. 11.
    Kleinberg, J., Tardos, E.: Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields. JACM 49(5), 616639 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts. IEEE Trans. PAMI 26, 147–159 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Leskovec, J., Krevl, A.: SNAP datasets: Stanford large network dataset collection (2014). http://snap.stanford.edu/data. Accessed May 2015
  14. 14.
    Levandoski, J.J., Sarwat, M., Eldawy, A., Mokbel, M.F.: Lars: a location-aware recommender system. In: 2012 IEEE 28th International Conference on Data Engineering, pp 450–461. IEEE, Washington, DC, USA (2012).  https://doi.org/10.1109/ICDE.2012.54
  15. 15.
    Li, K., Lu, W., Bhagat, S., Lakshmanan, L.V., Yu, C.: On social event organization. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. KDD ’14, pp 1206–1215. ACM, New York, NY, USA (2014).  https://doi.org/10.1145/2623330.2623724
  16. 16.
    Naor, J., Schwartz, R.: Balanced metric labeling. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing. STOC ’05, pp 582–591. ACM, New York, NY, USA (2005).  https://doi.org/10.1145/1060590.1060676
  17. 17.
    Orlin, J.B., Punnen, A.P., Schulz, A.S.: Approximate local search in combinatorial optimization. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA’04, pp. 587–596 (2004)Google Scholar
  18. 18.
    Rahn, M., Schäfer, G.: Efficient Equilibria in Polymatrix Coordination Games, pp. 529–541. Springer, Berlin (2015)zbMATHGoogle Scholar
  19. 19.
    Rother, C., Kolmogorov, V., Blake, A.: “GrabCut”-interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23(3), 309–314 (2004)CrossRefGoogle Scholar
  20. 20.
    Schaeffer, S.E.: Survey: graph clustering. Comput Sci Rev 1(1), 27–64 (2007).  https://doi.org/10.1016/j.cosrev.2007.05.001 CrossRefzbMATHGoogle Scholar
  21. 21.
    Wainwright, M., Jaakkola, T., Willsky, A.: Map estimation via agreement on trees: message-passing and linear programming. IEEE Trans. Inf. Theory 51, 3697–3717 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yedidia, J., Freeman, W., Weiss, Y.: Generalized belief propagation. In: Advances in Neural Information Processing Systems, pp. 689–695 (2000)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.HKUSTClear Water BayHong Kong
  2. 2.Hong Kong Science ParkShatinHong Kong

Personalised recommendations